The problem of portfolio management represents an important and challenging class of dynamic decision making problems, where rebalancing decisions need to be made over time with the consideration of many factors such as investors preferences, trading
environments, and market conditions. In this paper, we present a new portfolio policy network architecture for deep reinforcement learning (DRL)that can exploit more effectively cross-asset dependency information and achieve better performance than state-of-the-art architectures. In particular, we introduce a new property, referred to as textit{asset permutation invariance}, for portfolio policy networks that exploit multi-asset time series data, and design the first portfolio policy network, named WaveCorr, that preserves this invariance property when treating asset correlation information. At the core of our design is an innovative permutation invariant correlation processing layer. An extensive set of experiments are conducted using data from both Canadian (TSX) and American stock markets (S&P 500), and WaveCorr consistently outperforms other architectures with an impressive 3%-25% absolute improvement in terms of average annual return, and up to more than 200% relative improvement in average Sharpe ratio. We also measured an improvement of a factor of up to 5 in the stability of performance under random choices of initial asset ordering and weights. The stability of the network has been found as particularly valuable by our industrial partner.
This paper considers a life-time consumption-investment problem under the Black-Scholes framework, where the investors consumption rate is subject to a lower bound constraint that linearly depends on the investors wealth. Due to the state-dependent c
ontrol constraint, the standard stochastic control theory cannot be directly applied to our problem. We overcome this obstacle by examining an equivalent problem that does not impose state-dependent control constraint. It is shown that the value function is a third-order continuously differentiable function by using differential equation approaches. The feedback form optimal consumption and investment strategies are given. According to our findings, if the investor is more concerned with long-term consumption than short-term consumption, then she should, regardless of her financial condition, always consume as few as possible; otherwise, her optimal consumption strategy is state-dependent: consuming optimally when her financial condition is good, and consuming at the lowest possible rate when her financial situation is bad.
This paper develops the first closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expecte
d utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. We obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model, albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.
In recent years, cryptocurrencies have gone from an obscure niche to a prominent place, with investment in these assets becoming increasingly popular. However, cryptocurrencies carry a high risk due to their high volatility. In this paper, criteria b
ased on historical cryptocurrency data are defined in order to characterize returns and risks in different ways, in short time windows (7 and 15 days); then, the importance of criteria is analyzed by various methods and their impact is evaluated. Finally, the future plan is projected to use the knowledge obtained for the selection of investment portfolios by applying multi-criteria methods.
We present a reinforcement learning (RL) approach for robust optimisation of risk-aware performance criteria. To allow agents to express a wide variety of risk-reward profiles, we assess the value of a policy using rank dependent expected utility (RD
EU). RDEU allows the agent to seek gains, while simultaneously protecting themselves against downside events. To robustify optimal policies against model uncertainty, we assess a policy not by its distribution, but rather, by the worst possible distribution that lies within a Wasserstein ball around it. Thus, our problem formulation may be viewed as an actor choosing a policy (the outer problem), and the adversary then acting to worsen the performance of that strategy (the inner problem). We develop explicit policy gradient formulae for the inner and outer problems, and show its efficacy on three prototypical financial problems: robust portfolio allocation, optimising a benchmark, and statistical arbitrage
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance cri
terion based on the lower mean square error between the investors wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.
In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption and leisu
re, through the duality method. We impose different liquidity constraints over different time spans and conduct a sensitivity analysis to discover the effect of this kind of constraint.
Geometric Mean Market Makers (G3M) such as Uniswap, Sushiswap or Balancer are key building blocks of the nascent Decentralised Finance system. We establish non-arbitrage bounds for the wealth process of such Automated Market Makers in the presence of
transaction fees and highlight the dynamic of their so-called Impermanent Losses, which are incurred due to negative convexity and essentially void the benefits of portfolio diversification within G3Ms. We then turn to empirical data to establish if transaction fee income has historically been high enough to offset Impermanent Losses and allow G3M investments to outperform their continually rebalanced constant-mix portfolio counterparts. It appears that the median liquidity pool had a net nil ROI when taking Impermanent Losses into account. The cross-sectional dispersion of ROI has however been high and the pool net ROI ranking has been significantly autocorrelated for several weeks. This suggests that G3M pools are not yet efficiently arbitraged as agents may access ex-ante knowledge of which G3M pools are likely to be far better investment proposals than others. We finally focus on the UniswapV3 protocol, which introduced the notion of concentrated liquidity ranges and show that such a position can be replicated by leveraging a classic UniswapV2 pool while simultaneously hedging part of the underlying token price exposition. As such, the herein described Impermanent Loss dynamics also apply to UniswapV3 pools.
We study the cross-sectional returns of the firms connected by news articles. A conservative algorithm is proposed to tackle the type-I error in identifying firm tickers and the well-defined directed news networks of S&P500 stocks are formed based on
a modest assumption. After controlling for many other effects, we find strong evidence for the comovement effect between news-linked firms stock returns and reversal effect from lead stock return on 1-day ahead follower stock return, however, returns of lead stocks provide only marginal predictability on follower stock returns. Furthermore, both econometric and portfolio test reveals that network degree provides robust and significant cross-sectional predictability on monthly stock returns, and the type of linkages also matters for portfolio construction.
Harvey et al. (2010) extended the Bayesian estimation method by Sahu et al. (2003) to a multivariate skew-elliptical distribution with a general skewness matrix, and applied it to Bayesian portfolio optimization with higher moments. Although their me
thod is epochal in the sense that it can handle the skewness dependency among asset returns and incorporate higher moments into portfolio optimization, it cannot identify all elements in the skewness matrix due to label switching in the Gibbs sampler. To deal with this identification issue, we propose to modify their sampling algorithm by imposing a positive lower-triangular constraint on the skewness matrix of the multivariate skew- elliptical distribution and improved interpretability. Furthermore, we propose a Bayesian sparse estimation of the skewness matrix with the horseshoe prior to further improve the accuracy. In the simulation study, we demonstrate that the proposed method with the identification constraint can successfully estimate the true structure of the skewness dependency while the existing method suffers from the identification issue.
