Numerical and Optimization Techniques

◆ A probabilistic approach which transforms the stochastic process into a Markov chain and then applies Markov Decision Processes (MDP) which are based for their solutions on policy and value iteration algorithms (Kushner 1967, 1971, 1977).

◆ Discretization of the problem at hand, followed by the application of various techniques for the iterative solution of partial differential equations such as finite differencing, binomial trees, the finite element numerical technique and so on.

◆A third approach is based on the iterative solution of problems we know how to solve analytically (in particular, the linear quadratic problem). Such an approach is called perturbation techniques (Bensoussan 1982).

◆ A fourth approach is based on techniques and algorithms such as stochastic approximations (Kiefer and Wolfowitz 1952) and other related schemes.

◆Stochastic programming which transforms the stochastic optimization problems to nonlinear programming (Rockafellar and Wets, 1990, Varayia and Wets, 1989 and finally

◆ Simulation (Newman and Odell 1971, Rubenstein 1981) which can be applied in many different and creative ways.