UN NUEVO ACERCAMIENTO SOBRE LA MAXIMIZACIÓN DE CARTERAS DE INVERSIÓN PARA UNA MAYOR RENTABILIDAD EN LAS CONTRIBUCIONES

In this work, it showed how investment portfolios of a pension scheme are often maximized within the presence of return clause of contributions is presented. This clause permited return of accumulated contributions along side predetermined interest from harmless asset to members’ families whenever death occurs to their relations. Also considered herein are investments in cash, marketable security and loan to extend the entire accumulated funds of the pension scheme left to be distributed among the surviving members such the worth models of marketable security and loan followed geometric Brownian motions. the sport theoretic approach, separation of variable technique and mean variance utility were wont to obtain closed form solutions of the optimal control plans for the assets and therefore the efficient frontier. Next, the consequence of some parameters on the optimal control plans with time is numerically analysed. Furthermore, a theoretical comparison of our result with an existing result was given.En este trabajo, se mostró cómo se pueden maximizar las carteras de inversión de un plan de pensiones teniendo en cuenta una cláusula de devolución de contribuciones. Esta cláusula permitió la devolución de las contribuciones acumuladas junto con un interés predeterminado de un activo libre de riesgo, para aquellas familias el cual alguno de sus familiares haya fallecido. También se consideraron aquí las inversiones en efectivo, capital social y préstamos para aumentar los fondos totales acumulados del plan de pensiones que quedan por distribuir entre los miembros sobrevivientes, de modo que los modelos de precios de valores negociables y préstamos sigan movimientos geométricos brownianos. El enfoque de la teoría de juegos, la técnica de separación de variables y la utilidad de varianza media se utilizaron para obtener soluciones de forma cerrada de los planes de control óptimos para los activos y la frontera eficiente. Además, Se analizó numéricamente la insurgencia de algunos parámetros sobre los planes óptimos de control con el tiempo. Así como también, se ofrece una comparación teórica de nuestro resultado con un resultado existente

A defined benefit pension plan model with stochastic salary and heterogeneous discounting

We study the time-consistent investment and contribution policies in a defined benefit stochastic pension fund where the manager discounts the instantaneous utility over a finite planning horizon and the final function at constant but different instantaneous rates of time preference. This difference, which can be motivated for some uncertainties affecting payoffs at the end of the planning horizon, will induce a variable bias between the relative valuation of the final function and the previous payoffs and will lead the manager to show time-inconsistent preferences. Both the benefits and the contribution rate are proportional to the total wage of the workers that we suppose is stochastic. The aim is to maximize a CRRA utility function of the net benefit relative to salary in a bounded horizon and to maximize a CRRA final utility of the fund level relative to the salary. The problem is solved by means of dynamic programming techniques, and main results are illustrated numerically

MEAN VARIANCE OF FRACTIONAL STOCHASTIC MODEL AND LOGARITHM UTILITY OPTIMIZATION OF A PENSION FUND WITH TAX AND TRANSACTION COST

This work looked at the mean-variance of fractional continuous time stochastic model for the dynamics of a pension fund with tax and transaction cost, where the effect of tax and transaction cost charging makes on the expected logarithmic utility of the pensioner was established. The associated H-J-B equation in the optimization problem is obtained using lto’s lemma. An explicit solution to the pensioners’ problems was derived under stated condition

Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.jedc.2018.01.023 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/This paper provides a derivative-based optimal investment strategy for an ambiguity-adverse pension investor who faces not only risks from time-varying income and market return volatility but also uncertain economic conditions over a long time horizon. We derive a robust dynamic derivative strategy and show that the optimal strategy under ambiguity aversion reduces the exposures to market return risk and volatility risk and that the investor holds opposite positions for the two risk exposures. In the presence of a derivative, ambiguity has distinct effects on the optimal investment strategy. More important, we demonstrate the utility improvement when considering ambiguity and exploiting derivatives and show that ambiguity aversion and derivative trading significantly improve utility when return volatility increases. This improvement becomes more significant under ambiguity aversion over a long investment horizon.National Natural Science Foundation of China under Grant [71771220, 71721001, 71571195, 11371155, 11326199, 11771158]Major Program of the National Social Science Foundation of China [No. 17ZDA073]Fok Ying Tung Education Foundation for Young Teachers in the Higher Education Institutions of China [No. 151081]Guangdong Natural Science Foundation for Research Team [No. 2014A030312003]Guangdong Natural Science Funds for Distinguished Young Scholars [No. 2015A030306040]Natural Science Foundation of Guangdong Province of China [No. 2014A030310195]Insurance Society of China [No. ISCKT2016-N-l-07

Mathematical model of performance measurement of defined contribution pension funds

>Magister Scientiae - MScThe industry of pension funds has become one of the drivers of today’s economic activity by its important volume of contribution in the financial market and by creating wealth. The increasing importance that pension funds have acquired in today’s economy and financial market, raises special attention from investors, financial actors and pundits in the sector. Regarding this economic weight of pension funds, a thorough analysis of the performance of different pension funds plans in order to optimise benefits need to be undertaken. The research explores criteria and invariants that make it possible to compare the performance of different pension fund products. Pension fund companies currently do measure their performances with those of others. Likewise, the individual investing in a pension plan compares different products available in the market. There exist different ways of measuring the performance of a pension fund according to their different schemes. Generally, there exist two main pension funds plans. The defined benefit (DB) pension funds plan which is mostly preferred by pension members due to his ability to hold the risk to the pension fund manager. The defined contributions (DC) pension fund plan on the other hand, is more popularly preferred by the pension fund managers due to its ability to transfer the risk to the pension fund members. One of the reasons that motivate pension fund members’ choices of entering into a certain programme is that their expectations of maintaining their living lifestyle after retirement are met by the pension fund strategies. This dissertation investigates the various properties and characteristics of the defined contribution pension fund plan with a minimum guarantee and benchmark in order to mitigate the risk that pension fund members are subject to. For the pension fund manager the aim is to find the optimal asset allocation strategy which optimises its retribution which is in fact a part of the surplus (the difference between the pension fund value and the guarantee) (2004) [19] and to analyse the effect of sharing between the contributor and the pension fund. From the pension fund members’ perspective it is to define a optimal guarantee as a solution to the contributor’s optimisation programme. In particular, we consider a case of a pension fund company which invests in a bond, stocks and a money market account. The uncertainty in the financial market is driven by Brownian motions. Numerical simulations were performed to compare the different models

On the analysis and design of pension contracts from the customer's perspective

This thesis aims to design new long term investment structured products that can be used by insurance companies to smooth investment returns for their customers. These products are widely known as pension contracts as they are mainly used in the accumulation part of a pension scheme. Two popular pension schemes in UK are the Defined Benefit (DB) scheme and the Defined Contribution (DC) scheme. Recently, with the transition from the DB scheme to the DC scheme, more individuals must provide for their own retirement without the security of an employer-backed pension promise. Thus, it is of importance to provide the customer with suitable long term investment products. The thesis, consisting of three research papers, aims to show how to design a new pension contract that best meet the demand from the customers. In order to better understand the pension contracts, our first paper (Chapter 3) care fully examines a traditional with-profits contract in the market. This paper gives a closed form solution for the pricing of this contract and shows that it is overvalued to the customers because of its embedded guarantees. In addition, the smoothing method of this contract exposes the insurer to a risk that cannot be hedged. More over, the inter-generation risk sharing has been studied for this contract. The smoothing method, which is a typical feature of the with-profits products, is examined in detail in the second paper (Chapter 4). This paper compares three common smoothing methods of with-profits contracts in UK and see how the smoothing method performs. We not only compare the absolute terminal smoothed value, but also take the interim utility, customers’ satisfaction within the investment horizons, in to account. This has been done by using Multi-Cumulative Prospect theory (MCPT). The third paper (Chapter 5) propose a new pension contract with the features of guarantees and bonuses. It has transparent structure and clear distribution rule. Under Cumulative Prospect thoery (CPT), the new contract generates higher utility than the contract introduced in Guill´en et al. (2006). The result provides the evidence why the guarantees should be included in the pension contract. In addition, our result shows with the increase of policyholder’s investment horizons, the proportion of risky asset in the underlying investment portfolio increases while the proportion of risk free asset decreases. This result conforms to the traditional life cycle pension investment advice.Institute and Faculty of Actuaries - sponsorshi

The Valuation and Risk Management of a DB Underpin Pension Plan

Hybrid pension plans offer employees the best features of both defined benefit and defined contribution plans. In this work, we consider the hybrid design offering a defined contribution benefit with a defined benefit guaranteed minimum underpin. This study applies the contingent claims approach to value the defined contribution benefit with a defined benefit guaranteed minimum underpin. The study shows that entry age, utility function parameters and the market price of risk each has a significant effect on the value of retirement benefits. We also consider risk management for this defined benefit underpin pension plan. Assuming fixed interest rates, and assuming that salaries can be treated as a tradable asset, contribution rates are developed for the Entry Age Normal (EAN), Projected Unit Credit(PUC), and Traditional Unit Credit (TUC) funding methods. For the EAN, the contribution rates are constant throughout the service period. However, the hedge parameters for this method are not tradable. For the accruals method, the individual contribution rates are not constant. For both the PUC and TUC, a delta hedge strategy is derived and explained. The analysis is extended to relax the tradable assumption for salaries, using the inflation as a partial hedge. Finally, methods for incorporating volatility reducingand risk management are considered

Individual insurance choice: A stochastic control approach

This thesis applies the stochastic control approach to study the optimal insurance strategy for three problems. The first problem studies the optimal non-life insurance for an individual exhibiting internal habit formation in a life-cycle model. We show that the optimal indemnity is deductible under the expected premium principle. Under the additional assumption of exponential utility functions, we obtain the optimal strategies explicitly and find that habit formation reduces insurance coverage. Our model offers a potential explanation for the global underinsurance phenomenon. Some numerical examples and sensitivity analysis are presented to highlight our theoretical results. The second problem analyzes the optimal defined-contribution (DC) pension management under stochastic interest rates and expected inflation. Besides financial risk, we consider the mortality risk before retirement and introduce life insurance to the pension portfolio. We formulate this pension management problem by a Hamilton-Jacobi-Bellman (HJB) equation, derive its explicit solution, show the explicit solution's global existence, and prove the verification theorem. Our numerical research reveals that the pension member's demand for life insurance exhibits a hump shape with age and a ``double top'' pattern for the real short rates and expected inflation (high demand when the real short rates and expected inflation are both high or both low). These demand patterns are caused by the combined effects of the components in the optimal insurance strategy. The third problem is constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance