Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

Yang, Zhou; Liang, Gechun; Zhou, Chao

doi:10.1007/s11579-018-0232-5

Cited by 20 publications

(27 citation statements)

References 35 publications

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“…Since, by our construction, π * t = α * (t, u * t ) and u * t = β * (t, π * t ), it follows that (π * , u * ) is actually a saddle point for the associated game. However, compared to the classical saddle point argument such as Sion's Minimax Theorem (see, for example, [13,53]), our formulae are more explicit and is constructed via their corresponding counterstrategies.…”

Section: A Stochastic Differential Game Approachmentioning

confidence: 99%

“…Robust utility maximization in the optimal investment problems has been widely investigated under different situations with different approaches, among others, a stochastic control method in [10,26], a stochastic differential game approach in [48], a duality method in [49]. For more details on various portfolio selection problems, we refer to [1,14,20,21,27,53,54] and the references therein. In particular, we refer to [30,31,32] for the review of the recent advancements in robust investment management.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, if the game value exists, the optimal investment "strategy" corresponding to each scenario and the worst-case scenario under the optimal investment "strategy" are further given in ( 18)- (19). Compared to the saddle point argument used in [26,27,53] in the classical framework and [13] in the forward framework, our characterization (15)-( 16) and ( 18)-( 19) relies on the investor's response to each scenario and portfolio choice. Moreover, it is often relatively easy to compute the optimal strategies, as they only involve maximization/minimization problems rather than maxmin/minmax problems.…”

Section: Introductionmentioning

confidence: 99%

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A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Li¹,

Li²,

Liang³

2021

SIAM J. Finan. Math.

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This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.

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Section: A Stochastic Differential Game Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Li¹,

Li²,

Liang³

2021

SIAM J. Finan. Math.

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“…However, under clean price ,

{FVA}^{Δ}

still exists even when

L^{m} = 0

. This is one of the reasons why replacement cost should be discussed. (v)Considering different lending/borrowing not only makes the BSDEs for replication pricing semilinear, but also makes the associated Hamiltonians nonsmooth in optimal investment problems (see Bo, 2017; Bo & Capponi, 2016; Yang, Liang, & Zhou, 2019, for examples).…”

Section: Modelingmentioning

confidence: 99%

Binary funding impacts in derivative valuation

Lee¹,

Zhou

2020

Mathematical Finance

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We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, that is, one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semilinear backward stochastic differential equations (BSDEs) and partial differential equation (PDEs), and thus it is necessary to solve the equations numerically. However, once it can be guaranteed that only one of the rates affects pricing, linear equations can be recovered, and analytical formulae can be derived. Moreover, as a by‐product, our results explain how debt value adjustment (DVA) and funding benefits are dissimilar. It is often believed that considering both DVA and funding benefits results in a double‐counting issue but it will be shown that the two components are affected by different mathematical structures of derivative transactions. We find that funding benefit is related to the decreasing property of the payoff function, but this relationship decreases as the funding choices of underlying assets are transferred to repo markets.

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“…One mathematical difficulty to deal with the risk-sharing problem is that the amount by breach of contract is given by piece-wise concave functions. Mathematically similar problems were solved by [24,15,14,51]. In [24], portfolio optimization problems were considered where the agent switches utilities.…”

mentioning

confidence: 99%

A Risk-Sharing Framework of Bilateral Contracts

Lee¹,

Sturm²,

Zhou³

2020

SIAM J. Finan. Math.

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We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same pricing methodology and parameters. Thus, the two parties should enter the derivative contracts with a negotiated price, and we call the negotiation a risk-sharing problem. This framework defines the negotiation as a problem that maximizes the sum of utilities of the two parties. By the derived optimal price, we provide a theoretical analysis on how the price is determined between the two parties. As well as the price, the risk-sharing framework produces an optimal amount of collateral. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. However, inter-dealers markets are governed by regulations. As recommended in Basel III, it is a convention in inter-dealer contracts to pledge the full amount of a close-out price as collateral. In this case, using the optimal collateral, we interpret conditions for the full margin requirement to be indeed optimal.

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Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

Cited by 20 publications

References 35 publications

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Binary funding impacts in derivative valuation

A Risk-Sharing Framework of Bilateral Contracts

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