28 research outputs found
Portfolio optimization with Markov-modulated stock prices and interest rates
A financial market with one bond and one stock is considered where the risk free interest rate, the appreciation rate of the stock and the volatility of the stock depend on an external finite state Markov chain. We investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions. Due to explicit solutions it is possible to compare the value function of the problem to one where we have constant (average) market data. The case of benchmark optimization is also considered
Investment and Consumption with Regime-Switching Discount Rates
This paper considers the problem of consumption and investment in a financial
market within a continuous time stochastic economy. The investor exhibits a
change in the discount rate. The investment opportunities are a stock and a
riskless account. The market coefficients and discount factor switch according
to a finite state Markov chain. The change in the discount rate leads to time
inconsistencies of the investor's decisions. The randomness in our model is
driven by a Brownian motion and a Markov chain. Following Ekeland and Pirvu we
introduce and characterize the subgame perfect strategies. Numerical
experiments show the effect of time preference on subgame perfect strategies
and the pre-commitment strategies.Comment: arXiv admin note: substantial text overlap with arXiv:1107.189
Pairs Trading under Drift Uncertainty and Risk Penalization
In this work, we study a dynamic portfolio optimization problem related to
pairs trading, which is an investment strategy that matches a long position in
one security with a short position in another security with similar
characteristics. The relationship between pairs, called a spread, is modeled by
a Gaussian mean-reverting process whose drift rate is modulated by an
unobservable continuous-time, finite-state Markov chain. Using the classical
stochastic filtering theory, we reduce this problem with partial information to
the one with full information and solve it for the logarithmic utility
function, where the terminal wealth is penalized by the riskiness of the
portfolio according to the realized volatility of the wealth process. We
characterize optimal dollar-neutral strategies as well as optimal value
functions under full and partial information and show that the certainty
equivalence principle holds for the optimal portfolio strategy. Finally, we
provide a numerical analysis for a toy example with a two-state Markov chain.Comment: 24 pages, 4 figure
Risk-sensitive investment in a finite-factor model
A new jump diffusion regime-switching model is introduced, which allows for
linking jumps in asset prices with regime changes. We prove the existence and
uniqueness of the solution to the risk-sensitive asset management criterion
maximisation problem in this setting. We provide an ODE for the optimal value
function, which may be efficiently solved numerically. Relevant probability
measure changes are discussed in the appendix. The approach of Klebaner and
Lipster (2014) is used to prove the martingale property of the relevant density
processes.Comment: 23 pages, 1 figur
Multi-period mean-variance portfolio optimization with markov switching parameters
In this paper we deal with a multi-period mean-variance portfolio selection problem with the market parameters subject to Markov random regime switching. We analytically derive an optimal control policy for this mean-variance formulation in a closed form. Such a policy is obtained from a set of interconnected Riccati difference equations. Additionally, an explicit expression for the efficient frontier corresponding to this control law is identified and numerical examples are presented.Investiga-se um modelo multi-dimensional de seleção de carteiras em média-variância, no qual os parâmetros de mercado estão sujeitos a saltos Markovianos. Deriva-se analiticamente uma estratégia de controle ótima em forma fechada para esta formulação de média-variância. Esta estratégia é obtida através de um conjunto de equações a diferenças de Riccati. Adicionalmente, uma expressão explÃcita para a fronteira eficiente correspondente a este controle ótimo é identificada e exemplos numéricos são apresentados.(CNPq) Brazilian National Research Council(FAPESP) São Paulo Research Foundatio