RL approach for continuous-time mean-variance portfolio selection with empirical validation.
problem Continuous-time mean-variance portfolio selection in unknown market coefficients.
method Reinforcement learning for diffusion processes, sublinear regret bound derivation.
result RL strategy consistently outperforms model-based counterparts, especially in volatile markets.
RL approach to continuous-time MV portfolio selection with optimal policy being Gaussian.
problem Achieving optimal tradeoff between exploration and exploitation in continuous-time MV portfolio selection.
method Entropy-regularized, relaxed stochastic control problem; policy improvement theorem; RL algorithm.
result RL algorithm outperforms adaptive control and deep neural networks methods.
We consider continuous-time mean-variance portfolio selection with bankruptcy prohibition under convex cone portfolio constraints. This is a long-standing and difficult problem not only because of its theoretical significance, but also for its practical importance. First of all, we transform the above problem into an e…
This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of…
New method for portfolio management learns from past wealth evolution.
problem Optimizing portfolio selection based on past performance.
method Simulated annealing clustering for asset selection, considering past wealth evolution.
result Strategy effectively learns from past performance and performs well in practice.
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
Naive investors make riskier choices than optimal strategies in continuous-time finance.
problem Continuous-time Markowitz portfolio selection with naive reoptimization.
method Analytical derivation of naive policies from discretely naive policies.
result Naive policies are always riskier and less efficient than equilibrium policies.
Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal…
Study on optimal portfolio selection with varying borrowing and saving rates in continuous-time markets.
problem Optimal portfolio selection in markets with different borrowing and saving rates.
method Hamilton-Jacobi-Bellman equation, partial differential equation, verification argument.
result Existence and smoothness of the value function, identification of trading regions and strategies.
The paper solves portfolio selection for complex preferences in continuous time.
problem Dynamic portfolio selection for nonlinear preferences with time inconsistency.
method Stochastic maximum principle and verification theorems for equilibrium strategies.
result Equilibrium strategies derived in closed form for CRRA and CARA preferences.
Investment strategies for rank-dependent utility agents are derived in a continuous-time market.
problem Time inconsistency in rank-dependent utility models.
method Study of consistent planners seeking intra-personal equilibrium strategies.
result Explicit final wealth profile replicating equilibrium strategies, with scaling function derived.
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 be constructed using a limited number of fixed processes (mutual funds), for a m…
The paper proves the law of one price in a continuous-time setting without friction.
problem Identifying conditions under which the law of one price holds in a continuous-time setting without frictions.
method Formulating a new mechanism for LOP failure and proving a novel variant of the uniform boundedness principle.
result Establishes the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\scr{E}$-martingale state price density.
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. It turns out that the indirect utility functions inherit the…
Study optimal portfolio selection using average and current profitability of risky assets.
problem Continuous-time mean-variance portfolio selection in time-varying financial markets.
method Introduced AP and CP indexes; estimated AP and CP using second-order variation of an auxiliary wealth process.
result Estimations of AP and CP are more accurate than traditional MLE.
Paper uses RL to optimize multi-asset portfolios in fluctuating markets.
problem Optimizing multi-asset portfolios in time-varying financial markets.
method Soft Actor-Critic (SAC) algorithm for policy learning, policy iteration process.
result SAC algorithm outperforms in various criteria in simulated and real financial markets.
Investigates portfolio selection under rough volatility model, showing quadratic efficient frontier.
problem Mean-variance portfolio selection under rough volatility models.
method Constructs an auxiliary stochastic process to solve Riccati-Volterra equation for optimal strategy.
result MV efficient frontier is quadratic, influenced by roughness and volatility of volatility.
Study optimal investment strategies with entropy regularization in volatile markets.
problem Optimal portfolio selection under stochastic volatility with constraints.
method Entropy-regularized relaxed controls, dynamic programming, nonlinear PDEs.
result Existence of classical solutions to nonlinear HJB equation for value function.
It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local not…
We study a portfolio selection problem in a continuous-time Itô-Markov additive market with prices of financial assets described by Markov additive processes which combine Lévy processes and regime switching models. Thus the model takes into account two sources of risk: the jump diffusion risk and the regime switching …
Study on investment strategy for agents with periodic preferences and discounting.
problem Investment decisions by agents with periodic S-shaped preferences and present bias.
method Infinite-horizon, continuous-time portfolio selection problem with quasi-hyperbolic discounting.
result Time-consistent planning strategy can be formulated as an equilibrium to a static mean field game.
A framework for goal-based investing with penalties for fund transfers.
problem Investors' mental accounting and multiple investment goals.
method Continuous-time portfolio selection with mental costs and penalties.
result The value function is the unique solution to a complex system of equations.
This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…
Paper solves MV portfolio selection in jump-diffusion models with no-shorting constraint.
problem Mean-variance portfolio selection in jump-diffusion model with no-shorting constraint.
method Reduces problem to LQ control and finding a maximal point of a function, constructs viscosity solution.
result Explicit viscosity solution to Hamilton-Jacobi-Bellman equation, optimal controls derived.
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individu…
This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new generalized stochastic Riccati equations from which a candidate portfolio in feedback for…
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dy…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming {\it a priori} that the problem is well-pos…
Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortio…
Study on MMV in jump-diffusion models resolves MV's non-monotonicity issues.
problem Non-monotonicity and free cash flow stream problems in MV preferences.
method Explicit solution for MMV preferences in jump-diffusion models, proving non-negative potential measures.
result MMV resolves MV's non-monotonicity and free cash flow stream issues.
A new method for portfolio allocation in continuous-time markets.
problem Path-dependent portfolio allocation in continuous-time markets.
method Path-by-path framework, self-financing concept, partial differential equation, continuous-time algorithms.
result General explicit solution for wealth evolution in generic markets.
This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could…
Investigates mean-variance portfolio selection in non-Markovian markets.
problem Continuous-time Markowitz mean-variance portfolio selection in fake stationary affine Volterra models.
method Stochastic factor solution to a Riccati BSDE, deriving explicit solutions as multi-dimensional Riccati-Volterra equations.
result Analytical closed-form expressions for optimal portfolio policies and mean-variance efficient frontier.
Introduces SMMV preferences to avoid inconsistency in portfolio selection.
problem Monotone mean-variance preferences fail to differentiate strictly dominant payoffs.
method Introduces strictly monotone mean-variance preferences and applies them to portfolio selection problems.
result SMMV preferences provide a more rational basis for assessing prospects and coincide with MV preferences under certain conditions.
Paper explores arbitrage and CAPM in continuous time.
problem Understanding arbitrage and CAPM in continuous time.
method Analyzes instantaneous arbitrage and its relation to CAPM.
result Arbitrage and CAPM arguments differ in assumptions about the market portfolio.
The paper explores how investors make decisions under disappointment aversion, finding that they prefer not to invest.
problem Continuous-time portfolio selection under generalized disappointment aversion.
method Sufficient and necessary condition for equilibrium strategies via fully nonlinear integral equation.
result Equilibrium strategy under disappointment aversion leads to less investment in the stock market compared to classical utility theory.
New method controls renewable energy storage and portfolio selection with probabilistic constraints.
problem Control of McKean-Vlasov dynamics with probabilistic state constraints.
method Level-set approach for exact penalization and running maximum/integral cost.
result Extension to mean-field setting with machine learning algorithm.
Bayesian approach to portfolio selection reduces pessimism in frequent trading.
problem Tackling the challenge of estimating drift in Merton's portfolio selection model.
method Bayesian distributionally robust control with nonlinear Wasserstein projections.
result Reduced pessimism and improved performance in frequent rebalancing compared to existing methods.
This paper solves a financial portfolio selection problem in incomplete markets.
problem Portfolio selection in incomplete financial markets with ambiguity.
method Constructing an efficient frontier, simplifying the problem, introducing a new distorted Legendre transformation, and proving the bipolar relation and distorted duality theorem.
result The existence and uniqueness of optimal strategies are shown for different utility functions under specific conditions.
RL solves large-scale MV portfolio allocation with high returns.
problem Large-scale mean-variance portfolio optimization.
method Continuous-time reinforcement learning with a multivariate Gaussian policy.
result Our method outperforms econometric and deep RL methods by significant margins.
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. discrete-time two-asset markets under proportional transaction costs. We then extend ou…
RL for jump-diffusions applies to financial portfolio selection and option hedging.
problem Optimizing control in systems with jump-diffusion dynamics.
method Entropy-regularized exploratory control with stochastic policies, using existing diffusion algorithms with modifications.
result RL algorithms and parameterizations are invariant to jumps in jump-diffusion systems.
Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…
New framework optimizes multi-asset portfolio choice for high dimensions.
problem Optimizing high-dimensional continuous-time portfolio choice.
method Combines Pontryagin's Maximum Principle with BPTT for neural network policy learning.
result Achieves near-optimal policies with improved efficiency and precision.
A new model minimizes investment risk at multiple time points.
problem Minimizing risk in investment portfolios with multiple stopping points.
method Developed a multi-time state mean-variance model using Riccati equations.
result Optimal investment strategies can be derived from a sequence of Riccati equations.