A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future

Biffis, Enrico; Gołdys, Beniamin; Prosdocimi, Cecilia

doi:10.2139/ssrn.2607892

Cited by 5 publications

(16 citation statements)

References 43 publications

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“…The following Proposition, which is a direct consequence of Theorem 2.1 of [6], provides an explicit expression for the market value of human capital. Proposition 3.3.…”

Section: Rephrasing the No-borrowing Constraintmentioning

confidence: 95%

“…In particular, it implies that β > 0, and hence that the effective discount rate for labor income is positive (e.g., [17]). This allows us to apply Theorem 2.1 of [6], which is recalled, in the form we need here, in Proposition 3.3. When φ ≥ 0 a.e.…”

Section: Hypothesis 22mentioning

confidence: 98%

“…, ϕ n belonging to L 2 (−d, 0; R). This is the setup considered, for example, in [6] where no control problem is considered. In this paper, we consider path dependency in the drift of y only: the extension of our results to the above general case seems possible, although it would entail an increase in complexity of notation and technicalities.…”

Section: Hypothesis 22mentioning

confidence: 99%

“…In the next Section 2, we outline the model and provide the economic motivation for the setting. In Section 3, we rewrite the state equation (Subsection 3.1) by exploiting the representation of human wealth provided in [6], as well as the relevant state constraints (Subsection 3.2), both in an infinite dimensional setting where the states are Markovian. In Section 4, the core of the paper, we solve the problem explicitly after recalling the infinite dimensional formulation (Subsection 4.1):…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Portfolio Choice with Path Dependent Labor Income: the Infinite Horizon Case

Biffis¹,

Gozzi²,

Prosdocimi³

2020

SIAM J. Control Optim.

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“…The following Proposition, which is a direct consequence of Theorem 2.1 of [6], provides an explicit expression for the market value of human capital. Proposition 3.3.…”

Section: Rephrasing the No-borrowing Constraintmentioning

confidence: 95%

Section: Hypothesis 22mentioning

confidence: 98%

Section: Hypothesis 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Portfolio Choice with Path Dependent Labor Income: the Infinite Horizon Case

Biffis¹,

Gozzi²,

Prosdocimi³

2020

SIAM J. Control Optim.

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“…The following Proposition, which is a direct consequence of Theorem 2.1 of [6], provides an explicit expression for the market value of human capital. (25) and W solve the first of (11) with X 0 (t) in place of y(t).…”

Section: Rephrasing the No-borrowing Constraintmentioning

confidence: 95%

Optimal Portfolio Choice with Path Dependent Labor Income: The Infinite Horizon Case

Biffis¹,

Gozzi

Prosdocimi

2019

SSRN Journal

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We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.Key words: Stochastic functional (delay) differential equations; Optimal control problems in infinite dimension with state constraints; Second order Hamilton-Jacobi-Bellman equations in infinite dimension; Verification theorems and optimal feedback controls; Life-cycle optimal portfolio with labor income; Wages with path dependent dynamics (sticky).AMS classification: 34K50 (Stochastic functional-differential equations), 93E20 (Optimal stochastic control), 49L20 (Dynamic programming method), 35R15 (Partial differential equations on infinite-dimensional spaces), 91G10 (Portfolio theory), 91G80 (Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)) * Biffis

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Optimal portfolio choice with path dependent benchmarked labor income: a mean field model

Djehiche¹,

Gozzi²,

Zanco³

et al. 2020

Preprint

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We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjust slowly to financial market shocks, a feature already considered in Biffis et al. (2015) [8]. Second, the labor income yi of an agent i is benchmarked against the labor incomes of a population y n := (y1, y2, . . . , yn) of n agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when n → +∞ so that the problem falls into the family of optimal control of infinite dimensional McKean-Vlasov Dynamics, which is a completely new and challenging research field.We study the problem in a simplified case where, adding a suitable new variable, we are able to find explicitly the solution of the associated HJB equation and find the optimal feedback controls. The techniques are a careful and nontrivial extension of the ones introduced in the previous papers of Biffis et al.,[8,7].

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A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future

Cited by 5 publications

References 43 publications

Optimal Portfolio Choice with Path Dependent Labor Income: the Infinite Horizon Case

Optimal Portfolio Choice with Path Dependent Labor Income: the Infinite Horizon Case

Optimal Portfolio Choice with Path Dependent Labor Income: The Infinite Horizon Case

Optimal portfolio choice with path dependent benchmarked labor income: a mean field model

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