Topics in portfolio management

In this thesis, two topics in portfolio management have been studied: utility-risk portfolio selection and a paradox in time consistency in mean-variance problem. The first topic is a comprehensive study on utility maximization subject to deviation risk constraints. Under the complete Black-Scholes framework, by using the martingale approach and mean-field heuristic, a static problem including a variational inequality and some constraints on nonlinear moments, called Nonlinear Moment Problem, has been obtained to completely characterize the optimal terminal payoff. By solving the Nonlinear Moment Problem, the various well-posed mean-risk problems already known in the literature have been revisited, and also the existence of the optimal solutions for both utility-downside-risk and utility-strictly-convex-risk problems has been established under the assumption that the underlying utility satisfies the Inada Condition. To the best of our knowledge, the positive answers to the latter two problems have long been absent in the literature. In particular, the existence of an optimal solution for utility-semivariance problem, an example of the utility-downside-risk problem, is in substantial contrast to the nonexistence of an optimal solution for the mean-semivariance problem. This existence result allows us to utilize semivariance as a risk measure in portfolio management. Furthermore, it has been shown that the continuity of the optimal terminal wealth in pricing kernel, thus the solutions in the binomial tree models converge to the solution in the continuous-time Black-Scholes model. The convergence can be applied to provide a numerical method to compute the optimal solution for utility-deviation-risk problem by using the optimal portfolios in the binomial tree models, which are easily computed; such numerical algorithm for optimal solution to utility-risk problem has been absent in the literature. In the second part of this thesis, a paradox in time consistency in mean-variance has been established. People often change their preference over time, so the maximizer for current preference may not be optimal in the future. We call this phenomenon time inconsistency or dynamic inconsistency. To manage the issues of time inconsistency, a game-theoretic approach is widely utilized to provide a time-consistent equilibrium solution for dynamic optimization problem. It has been established that, if investors with mean-variance preference adopt the equilibrium solutions, an investor facing short-selling prohibition can acquire a greater objective value than his counterpart without the prohibition in a buoyant market. It has been further shown that the pure strategy of solely investing in bond can sometimes simultaneously dominate both constrained and unconstrained equilibrium strategies. With numerical experiments, the constrained investor can dominate the unconstrained one for more than 90% of the time horizon. The source of paradox is rooted from the nature of game-theoretic approach on time consistency, which purposely seeks for an equilibrium solution but not the ultimate maximizer. Our obtained results actually advocate that, to properly implement the concept of time consistency in various financial problems, all economic aspects should be critically taken into account at a time.Open Acces

Lycium barbarum Extracts Protect the Brain from Blood-Brain Barrier Disruption and Cerebral Edema in Experimental Stroke

BACKGROUND AND PURPOSE: Ischemic stroke is a destructive cerebrovascular disease and a leading cause of death. Yet, no ideal neuroprotective agents are available, leaving prevention an attractive alternative. The extracts from the fruits of Lycium barbarum (LBP), a Chinese anti-aging medicine and food supplement, showed neuroprotective function in the retina when given prophylactically. We aim to evaluate the protective effects of LBP pre-treatment in an experimental stroke model. METHODS: C57BL/6N male mice were first fed with either vehicle (PBS) or LBP (1 or 10 mg/kg) daily for 7 days. Mice were then subjected to 2-hour transient middle cerebral artery occlusion (MCAO) by the intraluminal method followed by 22-hour reperfusion upon filament removal. Mice were evaluated for neurological deficits just before sacrifice. Brains were harvested for infarct size estimation, water content measurement, immunohistochemical analysis, and Western blot experiments. Evans blue (EB) extravasation was determined to assess blood-brain barrier (BBB) disruption after MCAO. RESULTS: LBP pre-treatment significantly improved neurological deficits as well as decreased infarct size, hemispheric swelling, and water content. Fewer apoptotic cells were identified in LBP-treated brains by TUNEL assay. Reduced EB extravasation, fewer IgG-leaky vessels, and up-regulation of occludin expression were also observed in LBP-treated brains. Moreover, immunoreactivity for aquaporin-4 and glial fibrillary acidic protein were significantly decreased in LBP-treated brains. CONCLUSIONS: Seven-day oral LBP pre-treatment effectively improved neurological deficits, decreased infarct size and cerebral edema as well as protected the brain from BBB disruption, aquaporin-4 up-regulation, and glial activation. The present study suggests that LBP may be used as a prophylactic neuroprotectant in patients at high risk for ischemic stroke.published_or_final_versio

Mean variance portfolio management : time consistent approach

In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Björk and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Björk et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding “optimal” wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such “bankruptcy” solution can converge to the solution in continuous counterpart as Björk et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Björk et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting.published_or_final_versionMathematicsMasterMaster of Philosoph

Mean variance portfolio management : time consistent approach

In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Björk and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Björk et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding “optimal” wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such “bankruptcy” solution can converge to the solution in continuous counterpart as Björk et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Björk et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting.published_or_final_versionMathematicsMasterMaster of Philosoph

Topics in portfolio management

abstractStatistics and Actuarial ScienceDoctoralDoctor of Philosoph

Joint-preserving Tumor Resection and Reconstruction Using Image-guided Computer Navigation

Abstract Background Joint-preserving surgery is performed in select patients with bone sarcomas of extremities and allows patients to retain the native joint with better joint function. However, recurrences may relate to achieving adequate margins and there is frequently little room for error in tumors close to the joint surface. Further, the tumor margin on preoperative CT and/or MR images is difficult to transpose to the actual extent of tumor in the bone in the operating room. Questions/purposes We therefore determined whether joint-preserving tumor surgery could be performed accurately under image-guided computer navigation and determined local recurrences, function, and complications. Methods We retrospectively studied eight patients with bone sarcoma of extremities treated surgically by navigation with fused CT-MR images. We assessed the accuracy of resection in six patients by comparing the cross sections at the resection plane with complementary prosthesis templates. Mean age was 17 years (range, 6-46 years). Minimum followup was 25 months (mean, 41 months; range, 25-60 months). Results The achieved resection was accurate, with