Abstract
This paper proposes an approximation method to create an optimal continuous-time portfolio strategy based on a combination of neural networks and Monte Carlo, named NNMC. This work is motivated by the increasing complexity of continuous-time models and stylized facts reported in the literature. We work within expected utility theory for portfolio selection with constant relative risk aversion utility. The method extends a recursive polynomial exponential approximation framework by adopting neural networks to fit the portfolio value function. We developed two network architectures and explored several activation functions. The methodology was applied on four settings: a 4/2 stochastic volatility (SV) model with two types of market price of risk, a 4/2 model with jumps, and an Ornstein–Uhlenbeck 4/2 model. In only one case, the closed-form solution was available, which helps for comparisons. We report the accuracy of the various settings in terms of optimal strategy, portfolio performance and computational efficiency, highlighting the potential of NNMC to tackle complex dynamic models.
Highlights
Management 14: 322. https://Optimally allocating a collection of financial investments such as stocks, bonds and commodities has been a topic of concern to financial institutions and shareholders at least since the pioneering work of Markowitz’s mean-variance portfolio theory in 1952.People realized the potential of diversification and their work laid the foundations for the development of portfolio analysis in both academia and industry
These initial results were in discrete-time, but it was not long before continuous-time portfolio decisions were produced in the alternative paradigm of expected utility theory, as can be seen in Merton (1969)
The author assumed that the investor is able to continuously adjust their position, and the stock price process is modelled by a geometric Brownian motion (GBM)
Summary
Allocating a collection of financial investments such as stocks, bonds and commodities has been a topic of concern to financial institutions and shareholders at least since the pioneering work of Markowitz’s mean-variance portfolio theory in 1952. For the commodities asset class, Chiu and Wong (2013) modelled a mean-reverting risky asset by an exponential Ornstein–Uhlenbeck (OU) process and solved the investment problem for an insurer subject to the random payment of insurance claim These models are particular cases of the quadratic-affine family (see Liu (2006)), one of the broadest models solvable in closed-form. In this paper, motivated by the lack of knowledge on the correct expression for the portfolio value function for unsolvable models, we approximated the optimal portfolio strategy for any given stochastic process model with a neural network fitting the value function.
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