Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem

Cong, Fei; Oosterlee, Cornelis W.

doi:10.2139/ssrn.2563049

Cited by 5 publications

(5 citation statements)

References 25 publications

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“…In general, we can settle this problem by using a very large number of simulations, which is however expensive. In our numerical approach we always use the "regress-later" technique as applied in Cong and Oosterlee (2015).…”

Section: Backward Programming Algorithmmentioning

confidence: 99%

Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation

Cong

Oosterlee

2016

Journal of Economic Dynamics and Control

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a b s t r a c tWe propose a simulation-based approach for solving the constrained dynamic meanvariance portfolio management problem. For this dynamic optimization problem, we first consider a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a forward fashion. Then, based on this fast yet sub-optimal strategy, we propose a backward recursive programming approach to improve it. We design the backward recursion algorithm such that the result is guaranteed to converge to a solution, which is at least as good as the one generated by the multi-stage strategy. In our numerical tests, highly satisfactory asset allocations are obtained for dynamic portfolio management problems with realistic constraints on the control variables.

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Section: Backward Programming Algorithmmentioning

confidence: 99%

Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation

Cong

Oosterlee

2016

Journal of Economic Dynamics and Control

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“…Brandt et al (2005), inspired by the least-squares Monte Carlo method (see Longstaff and Schwartz (2001)), recursively estimated the value function and optimal allocation following a dynamic programming principle. This method was later named the BGSS and Cong and Oosterlee (2017) utilized the stochastic grid bundling method for conditional expectation estimation, introduced in Jain and Oosterlee (2015), further enhancing the accuracy of BGSS. Additionally, Zhu and Escobar-Anel (2022) targeted unsolvable continuous-time models, proposing an efficient and accurate simulation-based method, namely the polynomial affine method for constant relative risk aversion utility (PAMC).…”

Section: Introductionmentioning

confidence: 99%

Optimal market completion through financial derivatives with applications to volatility risk

Davison¹,

Escobar‐Anel²,

Zhu³

2022

Preprint

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This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to generalized diffusion models, to approximate the optimal derivatives-based portfolio strategy. We build upon the double optimization approach (i.e. expected utility maximization and risk exposure minimization) proposed in Escobar-Anel et al. (2022); demonstrating that strangle options are the best choices for market completion within equity options. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when only longterm maturity equity options are available.

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“…Cong and Oosterlee (2016) use a multistage strategy to perform forward simulation of control variables which are iteratively updated in the backward recursive program, where the admissible control sets are constructed as small neighborhoods of the solutions to the multi-stage strategy. Later, Cong and Oosterlee (2017) combine Jain and Oosterlee (2015)'s stochastic bundling technique with Brandt et al (2005)'s method. To sum up, these three papers have opened the way to the use of the LSMC algorithm for solving dynamic portfolio selection problems, but are at this stage still limited and constrained in their possible formulations of transaction cost, liquidity cost and market impact.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Langrené

Tian

et al. 2018

Quantitative Finance

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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.The effect of liquidity on the design of dynamic multi-period portfolio selection methods (a.k.a. asset allocation, portfolio optimization or portfolio management) has drawn great attention from academics and practitioners alike. Liquidity affects portfolio allocation in two main ways: temporary liquidity cost and permanent market impact. Liquidity cost, also known as implementation shortfall, temporary market impact or transitory market impact, is the difference between the realized transaction price and the pre-transaction price. Market impact is the permanent shift in the asset price after a transaction, due to the post-transaction "resilience" of the limit order book. These liquidity effects depend on several factors, such as the nature of the exchange platform, the duration of the trade execution, the transaction volume, the asset volatility and so on. Up to now, liquidity modeling for dynamic portfolio selection has been impeded by the intractability of analytical solutions and by the limited capability of numerical methods to handle endogenous stochastic prices. The purpose of the present paper is to introduce a new simulation-and-regression method capable of handling multivariate portfolio allocation problems under general transaction costs, liquidity costs and market impacts. The original literature on dynamic portfolio selection started with simple problems without transaction costs. The seminal papers, Mossin (1968), Samuelson (1969), Merton (1969) and Merton (1971) provide closed-form solutions of optimal asset allocation strategies for long-term investors. In reality though, every transaction incurs commission fee (or brokerage cost), and several improvements have therefore been proposed to account for transaction cost. Examples of closed-form solutions are Davis and Norman (1990), Shr...

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Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem

Cited by 5 publications

References 25 publications

Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation

Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation

Optimal market completion through financial derivatives with applications to volatility risk

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

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