Market Risk Control in Flexible Investment Decisions

Abstract

This chapter introduces models for risk control in investment decisions when the exit time of an investment is flexible, and the methods for solving these investment models.

Because the investment term is not fixed in flexible investments, Sect. 5.1 modifies the concept of return for flexible investments, an average profit rate is defined so that the return can be taken as the expected average profit rate.

Section 5.2 presents two kinds of optimization models for flexible investment decision problems. The first kind of models is for the situation where exit time of the investment can be taken as a random variable, investors only want to allocate their investment funds. The M-PVaR model and the M-risk model are proper models for investment decision in this situation. While the second kind of models is for the situation where exit time of the investment is taken as a decision variable, investors want to decide the allocation of investment fund and the exit time as well. Since the exit time is now a deterministic variable, risk indices introduced in Chap. 2 apply to this situation, investment decision problems can be formulated with the M-risk(t) model.

Section 5.3 introduces two methods for solving the PVaR minimization model, one method solves the model by solving a mixed integer programming, while the other method uses the soft optimization approach to solve the model.

Section 5.4 presents methods for solving the M-risk model under different information about the exit time and different assumptions about risk factors of investments.

Section 5.5 explains M-risk(t) models and methods for solving these models. Examples of solving the MV(t) model and the M-CVaR(t) model are included for the purpose of illustration.