Long-Term Optimal Investment in Matrix Valued Factor Models

Abstract. In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The supperdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein-Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein-Zin aggregator is neither Lipschitz nor jointly concave in all its variables.

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“…This strategy has been applied to portfolio optimization problems for time separable utilities, cf. [18] and [37].…”

Section: Consumption Investment Optimizationmentioning

confidence: 99%

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

Xing

2016

Finance Stoch

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105

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“…We borrowed this method from Chapter 10 of Stroock and Varadhan (2006). The readers can also refer to Robertson and Xing (2017) and Xing (2017) for more applications.…”

Section: The Verification Theoremmentioning

confidence: 99%

“…The solutions to this BSDE are unbounded and thereby the BMO argument breaks down. To proceed, we impose appropriate parameter conditions and overcome the difficulties by Lyapunov function argument, which is borrowed from Stroock and Varadhan (2006) and this method is utilized by Robertson and Xing (2017) for proving the optimality of the strategy before. Then the verification result can be confirmed carefully.…”

Section: Introductionmentioning

confidence: 99%

Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints

Feng¹,

Tian²

2021

Preprint

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In this paper, we investigate the consumption-investment problem for an investor with Epstein-Zin utility under general constraints. In an incomplete market, we impose closed, not necessarily convex, constraints on strategies and characterize optimal consumption and investment strategies via backward stochastic differential equations (BSDEs). Due to the stochastic environment of the market, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. We use the Lyapunov function to show a certain local martingale is a martingale and complete our proof by the martingale optimal principle. Finally, an explicit model is given to illustrate the main result.

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“…Davis & Lleo, 2015, for an overview in the jump-diffusion setting); and, as our results are valid for general factor processes, this technique is applicable to optimal investment and risk-sensitive control problems with matrix-valued factor process (cf. Buraschi, Porchia, & Trojani, 2010;Bäuerle & Li, 2013;Robertson & Xing, 2017), as well as jumps in asset prices.…”

Section: Introductionmentioning

confidence: 99%

Optimal investment and pricing in the presence of defaults

Ishikawa

Robertson

2019

Mathematical Finance

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We consider the optimal investment problem with random endowment in the presence of defaults. For an investor with constant absolute risk aversion, we identify the certainty equivalent, and compute prices for defaultable bonds and dynamic protection against default. This latter price is interpreted as the premium for a contingent credit default swap, and connects our work with earlier articles, where the investor is protected upon default. We consider a multiple risky asset model with a single default time, at which point each of the assets may jump in price. Investment opportunities are driven by a diffusion X taking values in an arbitrary region E⊆double-struckRd. We allow for stochastic volatility, correlation, and recovery; unbounded random endowments; and postdefault trading. We identify the certainty equivalent with a semilinear parabolic partial differential equation with quadratic growth in both function and gradient. Under minimal integrability assumptions, we show that the certainty equivalent is a classical solution. Numerical examples highlight the relationship between the factor process, market dynamics, utility‐based prices, and default insurance premium. In particular, we show that the holder of a defaultable bond has a strong incentive to short the underlying stock, even for very low default intensities.

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Long-Term Optimal Investment in Matrix Valued Factor Models

Cited by 7 publications

References 54 publications

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints

Optimal investment and pricing in the presence of defaults

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