Researches On Option Pricing And Related Problems Based On Uncertainty Theory

In real financial markets,asset prices are subject to a great deal of uncertainty due to the social environment and the credibility of investors,and uncertainty theory can effectively address such uncertainty problem.This paper presents an uncertain financial market model with memory characteristics by assuming that the dynamics of underlying asset,counterparty asset,and corporate liability are formulated by uncertain fractional differential equations of Caputo type and gives the vulnerable European call option price.Furthermore,in order to model the financial market with uncertainty,randomness and memory characteristics,this paper assumes that interest rate satisfies a stochastic differential equation,and gives the prices of European spread option and butterfly option.This paper studies the optimal investment and benefit strategies with background risks for defined contribution pension plan under uncertainty theory.Assuming that risky asset prices and income are uncertain processes with Heston volatility,we establish an uncertain Heston volatility optimal pension model with the real estate price variable and the salary variable as background-state variables by using the objective function of quadratic loss function.By solving the uncertain optimality equation,we obtain the optimal investment proportion and the optimal payment rate.Assuming that the underlying asset price follows the rough stochastic local volatility model,this paper applies the semimartingale and continuous-time Markov chain approximation analysis methods to give the approximate solutions for the arithmetic average Asian option prices with the help of double-Laplace transform and its numerical inverse transform.