A martingale characterization of consumption choices and hedging costs with margin requirements. (English) Zbl 1017.91061

Cuoco, Domenico; Liu, Hong

Math. Finance 10, No. 3, 355-385 (2000).

Investors who borrow in order to buy securities in the stock market are required to maintain a minimum amount of cash or securities with their broker-dealer. Such a requirement is called a margin requirement. In the paper the authors study the optimal consumption and investment choices and the cost of hedging European continget claims, given certain margin requirements. This problem without the margin rquirement constraint has been studied ealier by many authors [see, for example, I. Karatzas, J. P. Lehoczky, S. E. Shreve and G.-L. Xu, SIAM J. Control Optim. 29, 702-730 (1987; Zbl 0733.93085)]. Martingale techniques, similar to those employed in the reference cited above have been used to show the existence of optimal policies in the presence of margin requirements. Duality results are used to provide a characterization of optimal policies. An explicit solution is derived for an agent with a logarithmic utility.

Reviewer: Srinivas Raghava Mohan (New Delhi)

MSC:

91B42	Consumer behavior, demand theory
91B70	Stochastic models in economics

Keywords:

option pricing; portfolio optimization; optimal pricing; margin requirements; borrowing constraints; martingales; convex duality

Citations:

Zbl 0733.93085