苏州大学金融工程研究中心 “金融风险管理:理论与应用”系列专题报告

发布时间:2016-12-5 8:38:37 浏览次数:2557   

苏州大学金融工程研究中心金融风险管理:理论与应用系列专题报告。

报告时间:20161212日上午8:30-11:30

报告地点:苏州大学金融工程研究中心105学术报告厅

 

专题报告一:

报告题目:Optimal mean-variance reinsurance and investment in a jump-diffusion financial market with common shock dependence

报告人:南京师范大学 梁志彬 教授

 

专题报告二:

报告题目:Optimal financing of a firm: a hybrid strategy

报告人:中央财经大学 孟辉 教授

 

专题报告三:

报告题目:The optimal reinsurance and dividend with model uncertainty

报告人:中央财经大学 刘敬真 教授

 

专题报告四:

报告题目:Optimal timing for a company having  reinsurance

报告人:中央财经大学 李鹏  博士

 

专题报告五:

报告题目:Recursive Nonzero-sum Stochastic Differential Games

报告人:苏州大学 穆蕊  副教授

 

专题报告六:

报告题目:Pricing corporate bond and CDS under a structural form model with regime switching

报告人:苏州大学 王过京  教授

 

 

 

摘要:

 

Optimal mean-variance reinsurance and investment in a jump-diffusion financial market with common shock dependence

Zhibin Liang

School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, P.R.China

 

In this paper, we study the optimal reinsurance-investment problems in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process, and the two jump number processes are correlated by a common shock. Moreover, we remove the assumption of nonnegativity on the expected value of the jump size in the stock market, which is more economic reasonable since the jump sizes are always negative in the real financial market. Under the criterion of mean-variance, based on the stochastic linear-quadratic control theory, we derive the explicit expressions of the optimal strategies and value function which is a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. Furthermore, we extend the results in the linear-quadratic setting to the original mean-variance problem, and obtain the solutions of efficient strategy and efficient frontier explicitly. Some numerical examples are given to show the impact of model parameters on the efficient frontier.

 

 

 

Optimal financing of a firm: a hybrid strategy

Hui  Meng

China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China

 

Company or institution, in the form of cash. We first bring forward the decision maker can choose the types of injection capital including regular injection and impulse injection. The decision maker has the option to decide the capital injection rate and capital injection time and amount of impulse injection. Both of them have proportional cost, and fixed costs are considered in each impulse capital injection. The purpose of the decision maker is to find a strategy to minimize the cost of cash investment, but the constraint of the strategy is that it must ensure the firm has a positive cash flow. Under this rules, we analyze the optimal hybrid financing strategy dependent on the model cost parameters and show the sensibilities of the parameters to the optimal strategy and value function. (This is a joint work with Ming Zhou and Peng Li.)

 

 

 

The optimal reinsurance and dividend with model uncertainty

Jingzhen Liu

China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China

 

  In this talkwe analyze the optimal reinsurance and dividend problem   with model uncertainty for an insurer.  Here, the model uncertainty is  incorporated into the traditional diffusion surplus assumption, which denotes the possible deviation between the real market and the assumed model. We also include a penalty function in the objective function, which is denoted by a given function.  By choosing the reinsurance and the dividend strategy,  the objective is to maximize the expected discounted dividend before ruin in the worst case of all possible scenarios, namely, the worst market.  Using a dynamic programming approach, the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac (HJBI) equation with singular control. This problem is more difficult  than the traditional  robust  control  or singular control only. In this talk, we show that the value function is the unique solution of this HJBI with singular control. Moreover, we present a verification theorem if a smooth solution can be found. When  the function in the objective function is specified, we derive the closed-form solution.

 

 

Optimal timing for a company having  reinsurance

Peng Li

China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China

 

We examine a large insurance company whose cumulative cash flow process is described by a drifted Brownian motion. The decision maker has an option to purchase proportional reinsurance to maximize the survival probability or expected present value of dividend payments up to the time of ruin. A fixed transaction cost occurs at the beginning of a reinsurance treaty. This leads to the mixed problems among optimal stopping, regular and irregular stochastic control. We solve them by establishing a connection with optimal stopping problems and investigate the effect of fixed costs to optimal reinsurance policy of different objective functions. We find the conditions dependent on parameters of model and costs in which reinsurance is not valueless. Under these condition, we get the optimal time to purchase the reinsurance, optimal retained proportion, optimal dividend barrier, and the explicit expression of value function. In addition, some numerical examples are provided to show the effects of fixed costs on the value functions and the optimal policies.

 

 

 

 Recursive Nonzero-sum Stochastic Differential Games

                  Rui Mu

Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, P.R.China

 

Abstract: This talk is concerned with recursive nonzero-sum stochastic differential games in Markovian framework where the utilities are given by solutions of related BSDEs. We show the existence of a Nash equilibrium point for the game when the drift of the state process is no longer bounded under the generalized Isaacs assumption. The main tool is the notion of BSDEs which, in our case, are multidimensional with continuous coefficients. The generator is of stochastic linear growth on the volatility process and stochastic monotonic on the value process.

 

 

Pricing corporate bond and CDS under a structural form model with regime switching

Guojing Wang

Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, P.R.China

 

It is well known that the cycle of macro economy will impact on the credit quality of a defaultable firm. In this paper, we propose a new structural form credit risk model in which the market value of a defaultable firm is assumed to follow a geometric jump diffusion process with regime switching. We consider the influence of the macro economy on the corporate bond and its corresponding credit default swap (CDS). Closed form results  used for calculating the price and the fair premium are derived when the common distribution of jumps is double exponentially distributed. We use some historical data to calibrate model parameters. The numerical results show some certain accuracy of  prediction by the new model.

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