This paper proves the existence and uniqueness of solution optimal insurance problem with background risk presents explicit form solution.

This paper studies the pricing of Asian options when volatility underlying asset is uncertain. We use nonlinear Feynman-Kac formula in G-expectation theory to get two-dimensional PDEs. For arithmetic average fixed strike options, PDEs can be transferred linear floating we a dimension reduction technique transfer one-dimensional Then introduce applicable numerical computation methods for these two classes and analyze performance algorithms.

We study the credit risks of corporate debts using coherent risk measure ES(expected shortfall). Under our model, firms' value and their volatilities are solutions nonlinear equations. solve equations by Newton-Raphson method. With solutions, we can get distribution future value. Then estimate ES Richardson extrapolation Compared with repayment capability indicators, measured is consist real behavior firms. This shows effective.

We use the stochastic differential equations (SDE) driven by G‐Brownian motion to describe basic assets (such as stocks) price processes with volatility uncertainty. give estimation method of SDE’s parameters. Then, nonlinear Feynman‐Kac formula, we get partial satisfied derivatives. At last, a numerical scheme solve equations.

In this paper we establish a general swarm model with time delays under disturbances for the quadratic attractant/repellant profiles. It is proved that members will converge and form cohesive cluster around center in finite certain conditions presence of communication disturbances. For profiles, all to more favorable areas noise Numerical simulations illustrate theoretical results.

This study shows that, for a sequence of nonnegative valued measurable functions, convex combinations converges to function in the quasi-sure sense. can be used prove some existence results multiprobabilities models, and an example application finance is discussed herein.

This paper presents the integral(or differential) form of G-BSDEs, gives some kind apriori estimates their solutions, and under a very strong condition, proves G-martingale representation theorem, existence uniqueness theorem G-BSDEs.

In this paper, we define a dynamically consistent conditional G-expectation in space $\mathbb{L}^{p}$, and give the related stochastic calculus of It\^o's type, especially get formula for general $C^{1,2}$-function.

The aim of this paper is to explore the pricing Asian option by operator splitting methods. associate partial differential equation(PDE) a multi-dimensional problem. It not well adapted solution with simple numerical So we split PDE into two separate PDEs, one which Black-Scholes equation. Then introduce QUICK schemes calculate both equation and based on

The author considers the negative payoff sets, and constructs a coherent risk measure based on expected loss by option pricing method. Analyze credit risks of corporate debt, we find that payoffs creditor is like put seller. Therefore measurement can be in our model. We firms randomly chosen from Shanghai Stock Exchange, result show calculated are consistent with real behavior firms. So effective.

The pricing equations of the average options with jump diffusion processes can be formulated as two-dimensional partial integro-differential (PIDEs). In uncertain volatility model, for non-convex and non-concave payoffs, such butterfly spread, PIDEs are nonlinear. We use semi-Lagrangian method to reduce nonlinear PIDE a one-dimensional along trajectory price, Newton-type iteration guarantee convergence discrete solution viscosity solution. Monotonicity stability well results derived....

Portfolio optimization refers to the fact that investors allocate funds certain kinds of assets, so investment amount each type assets accounts for a proportion total investment.The purpose is make overall income held by as high possible, or risk low possible.With deepening people's research, theory portfolio has been gradually applied into more successful and mature theory.This paper intends use basic prospect model, using Matlab software, based on differential evolution algorithm, optimize...

Portfolio theory is one of the important directions financial research nowadays, its purpose to achieve maximum profit or minimum risk. since founding Von Neuman and Morgenstern (1947), Expected Utility has been widely used in decisionmaking investors. However, process portfolio, decision makers often aren't sure probability more interests. This uncertainty (or ambiguity) may affect preferences makers. Therefore, want add for ambiguity aversion analysis. In this paper, smooth model...