We consider a multi-stock market model. The processes of stock prices are governed by stochastic differential equations with stock return rates and volatilities driven by a finite-state Markov process. Each volatility is also disturbed by a Brownian motion; more exactly, it follows a...

We model reinsurance as a stochastic cooperation game in a continuous-time framework. Employing stochastic control theory and dynamic programming techniques, we study Pareto-optimal solutions to the game and derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation. After analyzing the...

We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to...

In this paper, a level set analysis is proposed which aims to analyze the S&P 500 return with a certain magnitude. It is found that the process of large jumps/drops of return tend to have negative serial correlation, and volatility clustering phenomenon can be easily seen. Then, a nonparametric...

In this paper, a level set analysis is proposed which aims to analyze the S&P 500 return with a certain magnitude. It is found that the process of large jumps/drops of return tend to have negative serial correlation, and volatility clustering phenomenon can be easily seen. Then, a nonparametric...

A microeconomic approach is proposed to derive the fluctuations of risky asset price, where the market participants are modeled as prospect trading agents. As asset price is generated by the temporary equilibrium between demand and supply, the agents' trading behaviors can affect the price...

Key Features:This book discusses some frontiers of Gaussian processes analysis and their associated Wick-Ito formula. For the first time, the studies of fractional Brownian motion is put into the framework of fractional white noise multiplication operatorsSome up-to-date treatment is of the...

We consider a problem of risk control and dividend optimization for a financial corporation facing a constant liability payment. More specifically we investigate the case of excess-of-loss reinsurance for an insurance company. In this scheme the insurance company diverts a part of its premium...