Optimal Portfolio Strategies with Stochastic Wage Income : The Case of A defined Contribution Pension Plan

We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market. The fund manager must cope with a set of stochastic investment opportunities and with the uncertainty involved by the labor market. After introducing a stochastic interest rate, we assume a market structure characterized by three assets : a riskless asset, a bond and a stock. Moreover, we introduce a stochastic process for salaries, and develop the model according to the stochastic dynamic programming methodology. We show that the optimal portofolio is formed by three components : a speculative component proportional to the market price of risk of the two risky assets through the relative risk aversion index, an hedging component proportional to the diffusion term of the interest rate, and a preference-free hedging component proportional to the volatilities of the salary process. Finally, after specifying a suitable fucntional form for the drift term of the salary process, we find a close form solution to the asset allocation problem.defined-contribution pension plan;salary risk;stochastic optimal control;Hamilton-Jacobi-Bellman equation

Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

In a financial market with one riskless asset and n risky assets following geometric Brownian motions, we solve the problem of a pension fund maximizing the expected CRRA utility of its terminal wealth. By considering a stochastic death time for a subscriber, we solve a unique problem for bot accumulation and decumulation phases. We show that the optimal asset allocation during these two phases must be different. In particular, during the first phase, the risky investment should increase through time because of closeness of death time. Our findings also suggest that it is not optimal to manage the two phases separately.pension funds; mortality risk; asset allocation

Optimal asset allocation for pension funds under mortality risk during the accumulation and ecumulation phases

In a financial market with one riskless asset and n risky assets following geometric Brownian motions, we solve the problem of a pension fund maximizing the expected CRRA utility of its terminal wealth. By considering a stochastic death time for a subscriber, we solve a unique problem for both accumulation and decumulation phases. We show that the optimal asset allocation during these two phases must be different. In particular, during the first phase the investment in the risky assets should decrease through time to meet future contractual pension payments while, during the second phase, the risky investment should increase through time because of closeness of death time. Our findings also suggest that it is not optimal to manage the two phases separately.pension fund; mortality risk; asset allocation

OPTIMAL PORTFOLIO STRATEGIES FOR DEFINED- CONTRIBUTION PENSION PLANS: A STOCHASTIC CONTROL APPROACH

2002/2003In questo lavoro consideriamo un modello stocastico per le scelte ottime di portafoglio del gestore di un fondo pensione a contributo definito. L'obiettivo del gestore sarà massimizzare l'utilità attesa della ricchezza finale del fondo stesso, cioè la ricchezza accumulata da un contribuente rappresentativo prima del suo pensionamento. Il modello classico di ottimizzazione dinamica, proposto inizialmente da Merton (1969, 1971), considera un mercato caratterizzato da una struttura piatta dei tassi di interesse. Tuttavia il problema dell'allocazione ottima delle risorse per un fondo pensione interessa intervalli di tempo relativamente lunghi, generalmente dai 20 ai 40 anni. Pertanto l'ipotesi di tassi di interesse costanti non risulta del tutto coerente con l'obiettivo del nostro studio. Per la stessa ragione, sembra opportuno introdurre nel modello di valutazione anche il rischio inflativo. A sostegno di questa ipotesi, come risulta da dati del Chicago Mercantile Exchange, alcuni tra i principali fondi pensione negli Stati Uniti attualmente investono dal 5 al 10 per cento del loro portafoglio in strumenti finanziari indicizzati all'inflazione. Inoltre, al fine di valutare i benefici associati ad un piano previdenziale, il gestore di un fondo pensioni si trova a dover considerare non solo rischi legati al mercato finanziario, ma anche altre variabili "esterne" al mercato stesso, per esempio legate al mercato del lavoro. Alla luce di quanto osservato finora, rispetto al modello classico di Merton includeremo nel problema di scelta ottima di portafoglio: (i) un processo stocastico per il tasso di interesse, (ii) il rischio inflativo, attraverso un processo stocastico che definisce l'indice dei prezzi al consumo e (iii) il "rischio salariale", attraverso un processo stocastico per i contributi. In particolare, metteremo ampiamente in evidenza come l'introduzione di flussi di cassa diversi da quelli legati al mercato finanziario (nel nostro caso i contributi) comporti notevoli ostacoli nella risoluzione del problema di ottimizzazione del portafoglio. Per risolvere il problema della scelta ottima di portafoglio di un fondo pensione seguiremo la teoria del controllo ottimo stocastico. Approcci alternativi (Deelstra e al., 2003, e Lioui e Poncet, 2001) sono basati sul "metodo della martingala" inizialmente introdotto da Cox e Huang (1989, 1991), i quali ottengono un'equazione alle derivate parziali (PDE) generalmente più semplice da risolvere di quella che si ottiene nella programmazione dinamica. Tuttavia, quando viene introdotto un processo stocastico per i salari, non è più possibile applicare direttamente tale metodologia. Nel primo capitolo della tesi presentiamo una rassegna degli strumenti matematici necessari per un'analisi formale dei modelli di allocazione ottima delle risorse in tempo continuo. Il Capitolo 2 introduce e descrive in fasi successive le principali caratteristiche dell'approccio del controllo ottimo stocastico nei problemi di consumo e investimento in tempo continuo. Nel Capitolo 3 descriviamo il modello di allocazione ottima delle risorse proposto da Merton (1969, 1971), il quale viene spesso indicato come la prima efficace applicazione del controllo stocastico in ambito economico. Nel contesto di tale modello, presentiamo una soluzione esplicita per funzioni di utilità con avversione assoluta al rischio iperbolica generalizzata. N el Capitolo 4 estendiamo il modello classico di M erto n al caso in cui i tassi di interesse sono stocastici . In particolare, mostriamo come l'introduzione nel problema di controllo ottimo di un'ulteriore variabile di stato (i tassi d'interesse stocastici), in aggiunta alla ricchezza, rappresenti un serio ostacolo nella risoluzione completa del modello. Sotto ipotesi opportune per la funzione valore, troviamo una soluzione esatta dell'equazione di Hamilton-Jacobi-Bellman associata al problema di controllo ottimo via Teorema di Feynman- Kac. In questo modo, siamo in grado di analizzare concretamente come la dinamica dei tassi di interesse condizioni la strategia ottima di investimento. In particolare, analizziamo come la presenza di una struttura stocastica per i tassi di interesse introduca nell'equazione del portafoglio ottimo una componente di hedging in aggiunta alla componente speculativa che caratterizza il modello di Merton. Il Capitolo 5 propone un modello di allocazione ottima delle risorse per un fondo pensione a contributo definito. Al fine di caratterizzare la fase di accumulazione del fondo, consideriamo il caso di un contribuente rappresentativo, il quale versa ad ogni epoca t E [O, T] una quota costante del proprio salario nel fondo stesso. Inizialmente, assumiamo un mercato finanziario completo e costituito da tre titoli: un titolo a rendimento certo, un'azione e un bond. Il 2 mercato è privo di opportunità di arbitraggio, non ci sono n costi di transazione n restrizioni sulla vendita allo scoperto dei titoli. A questo punto introduciamo i processi stocastici che definiscono l'indice dei prezzi al consumo e i salari. Come abbiano già sottolineato, proprio la presenza di un processo stocastico per i salari rappresenta il principale ostacolo nella risoluzione del problema di controllo ottimo. Infatti, quando introduciamo un processo dipendente da una fonte di rischio diversa da quelle che caratterizzano il mercato finanziario, il mercato cessa di essere completo. In questo caso, se da una parte è sempre possibile formalizzare il problema di controllo stocastico e definire l'equazione del portafoglio ottimo, dall'altra non siamo più in grado di applicare direttamente il Teorema di Feynman-Kac all'equazione di Hamilton-Jacobi-Bellman e quindi di esplicitare la funzione valore. Quindi, non ci è possibile studiare come la strategia ottima di portafoglio dipenda dai parametri del processo dei salari. Quello che noi proponiamo è un modello in cui la presenza di un processo stocastico per i salari è compatibile con l'ipotesi di mercato completo. Al fine di giustificare questo approccio, riconduciamo l'unica componente nonhedgeable del processo dei salari all'indice dei prezzi al consumo, il cui ruolo nel mercato finanziario verrà ampiamente discusso. In questo modo troviamo una soluzione in forma chiusa al problema di controllo ottimo e quindi siamo in grado di analizzare in dettaglio come le dinamiche stocastiche di salari e inflazione influenzino la composizione ottima del portafoglio. In particolare, dimostriamo che il portafoglio ottimo è caratterizzato da tre componenti: (i) una componente speculativa proporzionale sia all'indice di Sharpe, sia al reciproco dell'indice di avversione al rischio di Arrow-Pratt (coincidente con quella ottenuta nel modello di Merton), (ii) una componete di hedging dipendente dai parametri della variabili di stato (coincidente con quella ottenuta nel Capitolo 4) e (iii) una componente di hedging indipendente dall'attitudine al rischio e dipendente dai parametri di diffusione sia dei titoli finanziari sia dell'indice dei prezzi al consumo. Dopo aver esplicitato i valori attesi che caratterizzano la soluzione, mostriamo come il portafoglio ottimo possa essere semplificato nella somma di due componenti, di cui solo una dipende dall'orizzonte temporale. In questo modo otteniamo che una maggiore avversione al rischio assegna un peso maggiore alla componente dipendente dal tempo. Quindi, valori relativamente bassi del parametro di avversione al rischio determinano una strategia di portafoglio approssimativamente costante nel tempo. Concludiamo il capitolo presentando un'applicazione numerica del modello.This work contributes to the analysis of the asset allocation problem for pension funds in a stochastic continuous-time framework. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of the fund's terminal wealth, that is to say the wealth accumulated up to the retirement of a representative shareholder. We consider the case of a defined-contribution pension plan. The classical dynamic optimization model, initially proposed by Merton (1969, 1971), assumes a market structure with constant interest rate. We note that the optimal asset-allocation problem for a pension fund involves quite a long period, generally from 20 to 40 years. It follows that the assumption of constant interest rates does not fit with our target. For the same reason, we support the idea that also the inflation risk needs to be considered. According to this assumption, we observe that some of the leading pension funds in U.S. have from 5 to 10 percent of their portfolios allocated just to inflation-indexed instruments (Chicago Mercantile Exchange data). Moreover, the benefits proposed by DC pension plans often require the specification of the stochastic behavior of other variables, such as salaries. Thus, the fund manager must cope not only with financial risks, but also with other risk sources outside the financial market as for example salaries. In this case, we will highlight how the introduction of a stochastic non-financial incarne (in our case contribution) in the optimal portfolio problem causes several computational difficulties. Summing up the above considerations, with respect to the classical Merton's portfolio choice problem, here we include in the model: (i) a stochastic process for the short rate, (ii) the inflation risk, through a stochastic process for the consumer price index, and (iii) the salary risk, through a stochastic process for the contributions. The methodological approach we use to solve the optimal asset-allocation problem of a pension fund is the stochastic optimal control. Alternative approaches (see for instance Deelstra et al., 2003; and Lioui and Poncet, 2001) are based on the so-called "martingale approach" first introduced by Cox and Huang (1989, 1991), where the resulting partial differential equation is often simpler to salve than the Hamilton-Jacobi-Bellman equation coming from the dynamic programming. Nevertheless, in the martingale approach, when a stochastic process for salaries enters the optimization procedure, a submartingale is no more obtained to apply the theory. In the first chapter we present a review of the mathematical tools required for the formal analysis of asset allocation models in continuous-time. Chapter 2 illustrates the use of the stochastic optimal control as optimization engine in the consumption and portfolio choice problems in continuoustime. In Chapter 3 we develop the optimal consumption and investment problem presented by Merton ( 1969, 1971). This model is commonly regarded as the first successful application of stochastic control in economics. Moreover, we present an explicit solution to the control problem for generai hyperbolic absolute risk aversion utility functions. In Chapter 4 we extend the classical Merton's model by allowing interest rates to be stochastic. We illustrate how the introduction of another relevant state variable ( the stochastic short rate) in the control problem, in addition to the wealth, represents a delicate matter, although the methodological approach does not change. Under suitable assumptions on the value function, we derive an exact solution to the control problem by applying the Feynman-Kac Theorem directly to the Hamilton-Jacobi-Bellman equation. Then, we analyse how the short rate dynamics affects the optimal portfolio choice. Actually, the stochastic interest rate introduces a new hedging component in addition to the only speculative component characterizing the optimal portfolio strategy in the Merton's model. Finally, Chapter 5 extends the asset allocation models presented in the previous chapters to the case of a DC pension fund. In order to characterize the accumulation phase, we consider the case of a shareholder who, at each period t E [0, T], contributes a constant proportion of his salary to a personal pension fund. A t the time of retirement T, the accumulated pension fund will be converted into an annuity. Initially, we assume a complete financial market constituted by three assets: a riskless asset, a stock and a bond which can be bought and sold without incurring any transaction costs or restriction on short sales. Then, we take into account two stochastic processes describing the behavior of salaries and the consumer price index. As we have already remarked, the presence of a stochastic process for salaries represents the chief obstacle to a complete solution of the optimal control problem. In fact, if we assume that the salary process is driven by a risk source which does not belong to those defining the financial market, that is a non-hedgeable risk, we obtain that the market is no more complete. In this case, even if we can state the control problem, the corresponding Hamilton-Jacobi-Bellman equation an d the optimal portfolio, we are no t able to apply the Feynman-Kac Theorem and to find the optimal value function in a closed form. Therefore, this prevents us from studying how the coefficients of the salary process affect the optimal portfolio strategies. Here, we propose a model in which the presence of stochastic salaries is consistent with the assumption of complete market. In order to justify this proposition, we link the only non-hedgeable component of the salary process to the consumer price index, whose role in the financial market will be widely investigated. By following this way, we find a closed form solution to the control problem and then we are able to analyze in detail how the risk involved by the stochastic behavior of salary and inflation affects the optimal portfolio composition. We prove that the optimal portfolio is formed by three components: (i) a speculative component proportional to both the portfolio Sharpe ratio and the reciprocal of the Arrow-Pratt risk aversion index, as the one derived in the Merton's model, (ii) a hedging component depending on the state variable parameters as the one derived in Chapter 4, and (iii) a preference-free hedging component depending only on the diffusion terms of both the financial assets and the consumer price index. Furthermore, after working out the expected values characterizing the solution, the optimal portfolio can be simplified to the sum of only two components: one depending on the time horizon, and the other one independent of it. In particular, the optimal portfolio real composition turns out to have an absolutely time independent component. Moreover, the risk aversion parameter determines whether the portfolio is more or less affected by the time-dependent real component. The higher the risk aversion, the more the time-dependent real component affects the optimal portfolio. Accordingly, low values of the risk aversion parameter determine a real portfolio composition that becomes approximately constant through time. Finally, we present a numerical application in order to investigate the dynamic behavior of the optimal portfolio strategy more closely.XVII Ciclo1974Versione digitalizzata della tesi di dottorato cartacea

Oxidized Palladium Supported on Ceria Nanorods for Catalytic Aerobic Oxidation of Benzyl Alcohol to Benzaldehyde in Protic Solvents

In the present study, the catalytic activity of palladium oxide (PdOx) supported on ceria nanorods (CeO2-NR) for aerobic selective oxidation of benzyl alcohol (BnOH) to benzaldehyde (PhCHO) was evaluated. The CeO2-NR was synthesized hydrothermally and the Pd(NO3)2 was deposited by a wet impregnation method, followed by calcination to acquire PdOx/CeO2-NR. The catalysts were characterized by X-ray diffraction (XRD), temperature programmed reduction (TPR), transmission electron microscopy (TEM), Brunauer–Emmet–Teller (BET) surface area analysis, and X-ray photoelectron spectroscopy (XPS). In addition, the TPR-reduced PdOx/CeO2-NR (PdOx/CeO2-NR-Red) was studied by XRD, BET, and XPS. Characterizations showed the formation of CeO2-NR with (111) exposed plane and relatively high BET surface area. PdOx (x > 1) was detected to be the major oxide species on the PdOx/CeO2-NR. The activities of the catalysts in BnOH oxidation were evaluated using air, as an environmentally friendly oxidant, and various solvents. Effects of temperature and palladium oxidation state were investigated. The PdOx/CeO2-NR showed remarkable activity when protic solvents were utilized. The best result was achieved using PdOx/CeO2-NR and boiling ethanol as solvent, leading to 93% BnOH conversion and 96% selectivity toward PhCHO. A mechanistic hypothesis for BnOH oxidation with PdOx/CeO2-NR in ethanol is presente

Magnetic resonance imaging to assess cartilage invasion in recurrent laryngeal carcinoma after transoral laser microsurgery

Objective: To evaluate the diagnostic performance of magnetic resonance (MR) with surface coils in assessing cartilage invasion in recurrent laryngeal carcinoma after carbon dioxide transoral laser microsurgery (CO2 TOLMS). Methods: Two expert head and neck radiologists assessed cartilage invasion (infiltrated or non-infiltrated) in submucosal recurrences of laryngeal carcinoma after CO2 TOLMS: results were compared with histopathological report after salvage laryngectomy. Results: Thirty patients met the inclusion criteria and 90 cartilages were assessed. Overall sensitivity, specificity, and positive and negative predictive values for cartilage infiltration were 76, 93, 72 and 94%, respectively; for thyroid cartilage, the values were 82, 79, 69 and 88% respectively; for cricoid cartilage, all values were 100%; and for arytenoids, the values were 33, 96, 56 and 93% respectively. Conclusions: MR with surface coils was able to detect most thyroid and cricoid infiltration in the complex setting of post-CO2 TOLMS laryngeal carcinoma recurrence. In particular, the optimal performance in assessing cricoid invasion can be valuable in choosing the most appropriate treatment among total laryngectomy, open partial horizontal laryngectomies and non-surgical strategies

Exploring the Antitumor Potential of Copper Complexes Based on Ester Derivatives of Bis(pyrazol-1-yl)acetate Ligands

Bis(pyrazol-1-yl)acetic acid (HC(pz)(2)COOH) and bis(3,5-dimethyl-pyrazol-1-yl)acetic acid (HC(pz(Me2))(2)COOH) were converted into the methyl ester derivatives 1 (L-OMe) and 2 (L-2OMe), respectively, and were used for the preparation of Cu(I) and Cu(II) complexes 3-10. The copper(II) complexes were prepared by the reaction of CuCl2 center dot 2H(2)O or CuBr2 with ligands 1 and 2 in methanol solution. The copper(I) complexes were prepared by the reaction of Cu[(CH3CN)(4)]PF6 and 1,3,5-triaza-7-phosphaadamantane (PTA) or triphenylphosphine with L-OMe and L-2OMe in acetonitrile solution. Synchrotron radiation-based complementary techniques (XPS, NEXAFS, and XAS) were used to investigate the electronic and molecular structures of the complexes and the local structure around copper ions in selected Cu(I) and Cu(II) coordination compounds. All Cu(I) and Cu(II) complexes showed a significant in vitro antitumor activity, proving to be more effective than the reference drug cisplatin in a panel of human cancer cell lines, and were able to overcome cisplatin resistance. Noticeably, Cu complexes appeared much more effective than cisplatin in 3D spheroid cultures. Mechanistic studies revealed that the antitumor potential did not correlate with cellular accumulation but was consistent with intracellular targeting of PDI, ER stress, and paraptotic cell death induction

Prognostic Nomograms in Oral Squamous Cell Carcinoma: The Negative Impact of Low Neutrophil to Lymphocyte Ratio

Objectives: To investigate the prognostic significance of preoperative neutrophil to lymphocyte ratio (NLR) and the impact of different clinical-pathologic factors in a series of primary oral squamous cell carcinomas (OSCC).Materials and Methods: All naive OSCCs treated with upfront surgery between 2000 and 2014 were retrospectively reviewed. Patients with distant metastasis, synchronous head and neck cancer, immunological disorders, or who had received previous chemotherapy and/or radiation of the head and neck area were excluded. The main outcomes were overall (OS), disease-specific (DSS), loco-regional free (LRFS), and distant metastasis free (DMFS) survivals. Univariate (Kaplan-Meier) and multivariate (Cox regression model) analysis were performed, and nomograms developed for each outcome. NLR was analyzed as a continuous variable using restricted cubic spline multivariable Cox regression models.Results: One-hundred-eighty-two patients were included. Five-year estimates for LRFS, DMFS, DSS, and OS were 67, 83.7, 69.5, and 61.2%, respectively. NLR had a complex influence on survival and risk of recurrence: negative for very low and high values, while positive in case of intermediate ratios. At univariate analysis, T classification, 7th AJCC stage, nodal metastasis, perineural spread, and lymphovascular invasion were statistically significant. At multivariate analysis, extranodal extension (ENE) and perineural spread were the most powerful independent prognostic factors. NLR was an independent prognosticator for the risk of recurrence. In nomograms, NLR and ENE had the strongest prognostic effect.Conclusions: In OSCC, very low preoperative NLR values have a negative prognostic impact on survival and recurrence, similarly to high ratios. ENE and perineural spread are the most important clinical-pathologic prognosticators

The Peritoneum as a Natural Scaffold for Vascular Regeneration

Objective: The peritoneum has the same developmental origin as blood vessels, is highly reactive and poorly thrombogenic. We hypothesize that parietal peritoneum can sustain development and regeneration of new vessels. Methods and Results: The study comprised two experimental approaches. First, to test surgical feasibility and efficacy of the peritoneal vascular autograft, we set up an autologous transplantation procedure in pigs, where a tubularized parietal peritoneal graft was covered with a metal mesh and anastomosed end-to-end in the infrarenal aorta. Second, to dissect the contribution of graft vs host cells to the newly developed vessel wall, we performed human-to-rat peritoneal patch grafting in the abdominal aorta and examined the origin of endothelial and smooth muscle cells. In pig experiments, the graft remodeled to an apparently normal blood vessel, without thrombosis. Histology confirmed arterialization of the graft with complete endothelial coverage and neointimal hyperplasia in the absence of erosion, inflammation or thrombosis. In rats, immunostaining for human mitochondri revealed that endothelial cells and smooth muscle cells rarely were of human origin. Remodeling of the graft was mainly attributable to local cells with no clear evidence of c-kit+ endothelial progenitor cells or c-kit+ resident perivascular progenitor cells. Conclusions: The parietal peritoneum can be feasibly used as a scaffold to sustain the regeneration of blood vessels, whic