Multi-dimensional Volatility Model And Optimal Portfolio Of A Given Variance Budget

Option pricing theory is a hot issue in financial engineering research.Based on the theory of option pricing and financial stochastic analysis,this paper considers two main factors:given variance budget and option pricing.The paper discusses the expression form of value function and the corresponding optimal portfolio strategy under the multi-dimensional volatility model when the variance budget is given.In this paper,the method of option modeling is used to model and analyze the concerned problems,and then the theory of option pricing is used to discuss how to obtain the corresponding volatility value function and portfolio form by stochastic process analysis and calculation when variance budget is given.In the main part,the paper gives the asymptotic form of the corresponding value function and the specific expression of the optimal portfolio by using the option pricing theory under the model of the combination of fast factor,slow factor and fast and slow factor.The analysis of fast factor and slow factor is the basis of this paper,an important part of the subsequent analysis,and also the place where this paper takes a lot of time.Then,the paper gives the corresponding form of the conclusion and the asymptotic expression of the fast and slow factor model under the specific form.In the specific case,we also give some more meaningful proofs to carry out the auxiliary solution to the point of view of the paper.In the last part of the paper,we also put forward the specific form of the volatility model and the optimal portfolio under some substitution conditions,such as under the risk neutral condition and under the jump diffusion model.Through the option pricing theory,we get the corresponding form of value function and the relationship between the optimal portfolio strategy and the previous results.This paper is an innovation of mutual exchange about the combination of maturity date and given variance budget in option pricing.It is an extension of only discussing the content of option pricing.