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：2016年12月12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：Optimalmean-variance reinsurance and investment in a jump-diffusion financial marketwith 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 StochasticDifferential 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 withregime switching

报告人：苏州大学 王过京  教授

摘要：

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

Zhibin Liang

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

In this paper, we study the optimalreinsurance-investment problems in a financial market with jump-diffusion riskyasset, where the insurance risk model is modulated by a compound Poissonprocess, and the two jump number processes are correlated by a common shock.Moreover, we remove the assumption of nonnegativity on the expected value ofthe jump size in the stock market, which is more economic reasonable since thejump sizes are always negative in the real financial market. Under thecriterion of mean-variance, based on the stochastic linear-quadratic controltheory, we derive the explicit expressions of the optimal strategies and valuefunction which is a viscosity solution of the correspondingHamilton-Jacobi-Bellman equation. Furthermore, we extend the results in thelinear-quadratic setting to the original mean-variance problem, and obtain thesolutions of efficient strategy and efficient frontier explicitly. Somenumerical examples are given to show the impact of model parameters on theefficient frontier.

Optimal financing of a firm: a hybridstrategy

Hui  Meng

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

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

The optimalreinsurance and dividend with model uncertainty

JingzhenLiu

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

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

Optimal timing for a company having  reinsurance

Peng Li

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

We examine a large insurance company whose cumulativecash flow process is described by a drifted Brownian motion. The decision makerhas an option to purchase proportional reinsurance to maximize the survivalprobability or expected present value of dividendpayments up to the time of ruin. A fixed transaction cost occursat the beginning of a reinsurance treaty. This leads to the mixed problemsamong optimal stopping, regular and irregular stochastic control. We solve themby establishing a connection with optimal stopping problems and investigate theeffect of fixed costs to optimal reinsurance policy of different objectivefunctions. We find the conditions dependent on parameters of model and costs inwhich reinsurance is not valueless. Under these condition, we get the optimaltime to purchase the reinsurance, optimal retained proportion, optimal dividendbarrier, and the explicit expression of value function. In addition, somenumerical examples are provided to show the effects of fixed costs on thevalue functions and the optimal policies.

 RecursiveNonzero-sum Stochastic Differential Games

                  Rui Mu

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

Abstract: Thistalk is concerned with recursive nonzero-sum stochastic differential games in Markovianframework where the utilities are given by solutions of related BSDEs. We showthe existence of a Nash equilibrium point for the game when the drift of thestate process is no longer bounded under the generalized Isaacs assumption. Themain tool is the notion of BSDEs which, in our case, are multidimensional withcontinuous coefficients. The generator is of stochastic linear growth on thevolatility process and stochastic monotonic on the value process.

Pricingcorporate bond and CDS under a structural form model with regime switching

Guojing Wang

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

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