Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

Rongju Zhang, Nicolas Langrené (), Yu Tian, Zili Zhu, Fima Klebaner and Kais Hamza
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Rongju Zhang: Monash University [Melbourne]
Nicolas Langrené: CSIRO - Commonwealth Scientific and Industrial Research Organisation [Australia]
Yu Tian: Monash University [Melbourne]
Zili Zhu: CSIRO - Commonwealth Scientific and Industrial Research Organisation [Australia]
Fima Klebaner: Monash University [Melbourne]
Kais Hamza: Monash University [Melbourne]

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Abstract: We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impacts. To do so, we improve the accuracy of the control randomization approach in the case of discrete controls, and propose a global iteration procedure to further improve the allocation estimates. We validate our numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We quantify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic allocation protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk-aversion level and investment horizon.

Keywords: dynamic portfolio selection; portfolio optimization; transaction cost; liquidity cost; market impact; optimal stochastic control; switching cost; least squares Monte Carlo; simulation-and-regression (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-cmp and nep-ore
Note: View the original document on HAL open archive server: https://hal.science/hal-02909207v1
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Citations: View citations in EconPapers (4)

Published in Quantitative Finance, 2019, 19 (3), pp.519-532. ⟨10.1080/14697688.2018.1524155⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02909207

DOI: 10.1080/14697688.2018.1524155

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