An algorithm for construction of optimal timing solutions in problems with a stochastic payoff function

摘要

A dynamic model of optimal timing is applied to the problem of optimization of an innovation process in a competitive market environment. The basic element of the model is a block for optimization of the stopping time of the investment process. The problem of optimal timing is solved in parallel with adjoint problems of assessment of the market potential innovation and optimal control synthesis of the investment process. For construction of the optimal control synthesis the basic elements of models of optimal economic growth are used. In the econometric block, a probabilistic model is applied for design of market trajectories described by distribution functions. These distribution functions determine a market share of commercialized projects and probability of presence of competitors on the market at the current moment of time. Stochastic models for specification of the price formation mechanism are constructed for a series of distribution functions. An algorithm for construction of the optimal commercialization time and optimal investment plan is proposed. The algorithm is based on qualitative analysis of extremal points of the utility function which correspond to intersection points of a market distribution function and marginal costs of the innovation process. The algorithms are realized in the program software for simulation of optimal investment plans.