In this paper will be demonstrated that the link between optimal option value, risk measuring and risk managing is especially close, and it is given by stochastic optimization.
Post the financial crisis of 2008 it has been clear that risk considerations must enter into the valuation of derivatives, previously performed in an entirely "risk neutral world". The average value-at-risk is related to the problem of investor, which we use for option pricing. Let Y = (S-K)+ is payoff for call option, where strike price K and premium C is known to investor and distribution of underlying risky assets S is modeled. Suppose that an investor has to decide about the amount X of invest before the actual available income is given to him by random variable