Yulian Fan

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In this paper we establish a general swarm model with time delays under disturbances for the quadratic attractant/repellant profiles. It is proved that the swarm members will converge and form a cohesive cluster around the center in a finite time under certain conditions in the presence of communication delays and disturbances. For quadratic(More)
The aim of this paper is to explore the pricing of Asian option by operator splitting methods. The associate partial differential equation(PDE) is a multi-dimensional problem. It is not well adapted to solution with simple numerical methods. So we split the PDE into two separate PDEs, one of which is the Black-Scholes equation. Then we introduce QUICK(More)
We study the credit risks of corporate debts using the coherent risk measure of ES(expected shortfall). Under our model, the firms' value and their volatilities are the solutions of nonlinear equations. We solve the equations by the Newton-Raphson method. With the solutions, we can get the distribution of the firms' future value. Then we estimate the ES(More)
The author considers the negative payoff sets, and constructs a coherent risk measure based on expected loss by the option pricing method. Analyze the credit risks of the corporate debt, we find that the payoffs of the creditor is like that of the put option seller. Therefore the credit risk measurement can be put in our risk measure model. We measure the(More)
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