Relative growth optimal strategies in an asset market game
We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of a strategy, called relative growth optimal, such that the logarithm of the share of its wealth in the total wealth of the market is a submartingale for any strategies of the other investors. It is also shown that this strategy is asymptotically optimal in the sense that it achieves the maximal capital growth rate when compared to competing strategies. Based on the results obtained, we study the asymptotic structure of the market when all the investors use the relative growth optimal strategy.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Optimal growth strategies for a representative agent in a continuous-time asset market
We propose a multi-agent model of an asset market and study conditions that guarantee that the strategy of an individual agent cannot outperform the market. The model assumes a mean-field approximation of the market by c…
A continuous-time asset market game with short-lived assets
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth pr…
Ergodic robust maximization of asymptotic growth
We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ a…
Capital growth and survival strategies in a market with endogenous prices
We call an investment strategy survival, if an agent who uses it maintains a non-vanishing share of market wealth over the infinite time horizon. In a discrete-time multi-agent model with endogenous asset prices determin…
Investing for the Long Run
This paper studies long term investing by an investor that maximizes either expected utility from terminal wealth or from consumption. We introduce the concepts of a generalized stochastic discount factor (SDF) and of th…