Report by the Laboratory staff members at the "Tikhonov readings 2019" scientific conference at the Lomonosov Moscow State University
On October 28, the Laboratory staff member Andreev N.A. made a report "Portfolio Selection in an Illiquid Market in the Presence of Model Error" at the "Tikhonov readings 2019" scientific conference at the Lomonosov Moscow State University.
Overview of the report
The research considers the application of the guaranteed approach, proposed by Smirnov S.N., to the portfolio selection problem in an illiquid market in the presence of model error. We state the problem as a game against nature in discrete time with finite horizon, where the investor attempts to maximize the portfolio reward (in terms of the robust Savage equivalent) at the end of the investment horizon. Optiomal strategy can be found as the solution to the corresponding Bellman-Isaacs equation. Non-Markov dynamics of the system, a general transaction costs function and a price impact can be introduced into the framework. Under some mild assumptions we prove the the transaction costs function should be convex, we also obtain sufficient conditions for strict and strong convexity.
Numeric solution of the Bellman-Isaacs equation is time-consuming since it requires solving an addiditional minimizatiom subproblem at each step, where minimization is performed over the set of probability measures with the common support and expectation. We obtain sufficient conditions which allow the subproblem to be reduced to the minimization over the set of extreme points of the support.
The proposed approach might be useful when comparing the investment strategies or estimating the liquidation value of the portfolio in the presence of ambiguity in the market, e.g. during a financial crisis. The approach might also be relevant during the rebalancing of a large portfolio over a short period of time.
Link to the the Conference Program and the Proceedings (in Russian): https://cs.msu.ru/sites/cmc/files/attachs/tezisy_tch_2019_print.pdf