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：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 talk，we 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.