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Can deep reinforcement learning algorithms be exploited as solvers for optimal trading strategies? The aim of this work is to test reinforcement learning algorithms on conceptually simple, but mathematically non-trivial, trading…
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can…
The optimal allocation of assets has been widely discussed with the theoretical analysis of risk measures, and pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model. The $\alpha$-risk plays a…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…
In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to…
An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities, in the presence of small transaction costs and a binding exogenous portfolio…
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
Traders buy and sell financial instruments in hopes of making profit, and brokers are responsible for the transaction. There are several hypotheses and conspiracy theories arguing that in some situations, brokers want their traders to lose…
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level…
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The…
This scientific paper propose a novel portfolio optimization model using an improved deep reinforcement learning algorithm. The objective function of the optimization model is the weighted sum of the expectation and value at risk(VaR) of…
Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are $L_1$. We present a mean-field approach that reduces the multi-asset problem…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices…
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small…
When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
This paper studies the problem of maximizing expected utility from terminal wealth combining a static position in derivative securities, which we assume can be traded only at time zero, with a traditional dynamic trading strategy in stocks.…
In this paper, we propose a machine learning algorithm for time-inconsistent portfolio optimization. The proposed algorithm builds upon neural network based trading schemes, in which the asset allocation at each time point is determined by…
We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk…
In this paper we consider a discrete-time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log-return i.i.d. framework the solution to a suitable Bellman equation…