Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes

The Optimal Dividend Payout Model with Terminal Values and Its Application

For some firms with large nonliquid assets, preferred shareholders can still get back a little bit of money when the firms finish disbursement of loans at the status of bankruptcy. For such a situation, to investigate the optimal dividend policy, a stochastic dynamic dividend model with nonzero terminal bankruptcy values is put forward in this paper. Moreover, an analytic solution for the optimal objective function of the discounted dividends is provided and verified. An important application of this result is that it can be employed to construct the solution for the optimal value function on the dividend problem with bailouts at bankruptcy. Further, the relationship for the solutions of these two different problems is demonstrated. In the end, some numerical examples are provided to support our theoretical results and the corresponding economic interpretations are illustrated

Classical and impulse stochastic control on the optimization of the dividends for the terminal bankruptcy model and its application

Title from PDF of title page (University of Missouri--Columbia, viewed on December 7, 2010).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. Michael Taksar.Vita.Ph. D. University of Missouri--Columbia 2010.In this dissertation, I discuss the optimization of dividends of reinsurance companies with the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, meanwhile the tax rate and the In this dissertation, I discuss the optimization of dividends of reinsurance companies with the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, meanwhile the tax rate and the fixed transaction cost for each dividend are considered. The mathematical problem of maximizing the summation of expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, I reduce it to quasi-variational inequalities with nonzero boundary condition. The main contribution of this dissertation is to explicitly construct and verify solutions of these inequalities, and to consequently present the optimal policy. As an application, the solution of the optimization of dividends under the nonterminal bankruptcy model is provided in the end.Includes bibliographical reference

Probiotic Microbes Sustain Youthful Serum Testosterone Levels and Testicular Size in Aging Mice

The decline of circulating testosterone levels in aging men is associated with adverse health effects. During studies of probiotic bacteria and obesity, we discovered that male mice routinely consuming purified lactic acid bacteria originally isolated from human milk had larger testicles and increased serum testosterone levels compared to their age-matched controls. Further investigation using microscopy-assisted histomorphometry of testicular tissue showed that mice consuming Lactobacillus reuteri in their drinking water had significantly increased seminiferous tubule cross-sectional profiles and increased spermatogenesis and Leydig cell numbers per testis when compared with matched diet counterparts This showed that criteria of gonadal aging were reduced after routinely consuming a purified microbe such as L. reuteri. We tested whether these features typical of sustained reproductive fitness may be due to anti-inflammatory properties of L. reuteri, and found that testicular mass and other indicators typical of old age were similarly restored to youthful levels using systemic administration of antibodies blocking pro-inflammatory cytokine interleukin-17A. This indicated that uncontrolled host inflammatory responses contributed to the testicular atrophy phenotype in aged mice. Reduced circulating testosterone levels have been implicated in many adverse effects; dietary L. reuteri or other probiotic supplementation may provide a viable natural approach to prevention of male hypogonadism, absent the controversy and side-effects of traditional therapies, and yield practical options for management of disorders typically associated with normal aging. These novel findings suggest a potential high impact for microbe therapy in public health by imparting hormonal and gonad features of reproductive fitness typical of much younger healthy individuals.National Institutes of Health (U.S.) (Grant P30-ES002109)National Institutes of Health (U.S.) (Grant U01 CA164337)National Institutes of Health (U.S.) (Grant RO1CA108854

Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy

Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy

In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy

Relative Performance Concern on DC Pension Plan under Heston Model with Inflation Risk

With the global outbreak of new coronavirus pneumonia, more and more countries have entered the state of sealing off cities. After the epidemic, with the shortage of some materials, the economy is very likely to enter the state of inflation. Thereby, it is necessary and urgent for us to reconsider investment problems involving inflation risk. In this paper, we mainly study the optimal investment strategy of two defined contribution (DC) pension managers with strategy interaction under inflation risk. The traditional portfolio literatures mainly focus on DC pension plan and try to maximize the expected utility of terminal nominal wealth. In this paper, we consider the more complicated situation that pension managers have, both concerns on relative wealth and relative risk aversion. Then, the objective function is constructed to satisfy these two concerns. The dynamic programming principle method is employed to solve the above problems, and a series of analytical solutions to this problem are obtained. Finally, some numerical examples are discussed for the economic implications to support our theoretical results

Partnerships of Bidders with Constant Relative Risk Aversions

In this paper, we study a dynamic auction for allocating a single indivisible project while different participants have different bid values for the project. When the price rises continuously, the bidders can retreat the auction and obtain the compensation by the difference between the price at retreating time and the previous bid price. The final successful bidder achieves the project and pays compensations to others. We show that the auction of bidders with constant relative risk aversion (CRRA) has a unique equilibrium. While the relative risk aversion coefficient approaches to zero, the equilibrium with CRRA bidders would approach to the equilibrium with risk-neutral bidders