Related papers: Multi-time state mean-variance model in continuous…
Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration…
This is a companion paper of [Mixed equilibrium solution of time-inconsistent stochastic LQ problem, arXiv:1802.03032], where general theory has been established to characterize the open-loop equilibrium control, feedback equilibrium…
This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation…
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution…
In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where this objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the…
We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed…
We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading…
Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for…
We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary ($g_{ij}(t,x)\geq 0$). We show existence of the optimal strategy, and give when…
This paper investigates dynamic and static fund separations and their stability for long-term optimal investments under three model classes. An investor maximizes the expected utility with constant relative risk aversion under an incomplete…
Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2.…
We solve an infinite time-horizon bounded-variation stochastic control problem with regime switching between $N$ states. This is motivated by the problem of a government that wants to control the country's debt-to-GDP (gross domestic…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…
This paper presents an optimal strategy for portfolio liquidation under discrete time conditions. We assume that N risky assets held will be liquidated according to the same time interval and order quantity, and the basic price processes of…
We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider…
Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified…