On Market Completions Approach to Option Pricing

Option pricing is one of the most important problems contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging respect to a unique risk-neutral measure. In incomplete markets, an adequate achieved by determining interval prices as region negotiation between seller and buyer option. End points this characterise minimum maximum average discounted pay-off function over set equivalent measures. By estimating these end points, constructs super hedging strategies providing risk-management such contracts. The current paper analyses interesting approach problem, which consists introducing necessary amount auxiliary assets that market becomes determined. One estimate taking minimal maximal values from various numbers calculated help different completions. dual characterisation it described here detail for multivariate diffusion model. Besides that, discusses how method exploited optimal investment partial problems.