Inconsistent Investment and Consumption Problems

Kronborg, Morten Tolver; Steffensen, Mogens

doi:10.1007/s00245-014-9267-z

Cited by 34 publications

(35 citation statements)

References 8 publications

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“…Proof The proof of this theorem is similar to the proof of Theorem 2.1 of Björk et al (2014) or Theorem 2.1 of Kronborg & Steffensen (2015), so we omit it here.…”

Section: Verification Theoremmentioning

confidence: 91%

“…Therefore, we need to consider an optimization problem when the objective function changes over the time horizon and to obtain a corresponding optimal strategy. Björk et al (2014) and Kronborg & Steffensen (2015) study the problem in a game theoretic framework. That is, our preferences change in a temporally inconsistent way as time goes by and we can thus think about the problem as a game where the players are the future incarnations of ourselves.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Problem (3.1) is a static optimization problem as one determines the optimal strategy at the initial time 0. In Björk et al (2014) and Kronborg & Steffensen (2015), Problem (3.1) is called the mean-variance optimization problem with pre-commitment. The corresponding optimal strategy of (3.1) is called the optimal pre-commitment strategy.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Barro (1999), Karp (2007), Ekeland & Lazrak (2010), Ekeland & Pirvu (2008), Marin-Solano & Navas (2009, Ekeland et al (2012) further considered time-inconsistent preferences problems in different situations. Recently, there has been renewed interest in time-consistent mean-variance portfolio selection problem, see, for example, Björk & Murgoci (2009), Basak & Chabakauri (2010, Kryger & Steffensen (2010), Wang & Forsyth (2011), Czichowsky (2013, Björk et al (2014), Kronborg & Steffensen (2015). Zeng & Li (2011) considered the optimal time-consistent investment and reinsurance strategies for insurers under the mean-variance criterion with the Black-Scholes model.…”

Section: Introductionmentioning

confidence: 99%

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Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

Xiang

Qian

2015

Scandinavian Actuarial Journal

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We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset's price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsuranceinvestment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.

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“…Proof The proof of this theorem is similar to the proof of Theorem 2.1 of Björk et al (2014) or Theorem 2.1 of Kronborg & Steffensen (2015), so we omit it here.…”

Section: Verification Theoremmentioning

confidence: 91%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

Xiang

Qian

2015

Scandinavian Actuarial Journal

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“…Early papers in mathematical finance to study the game-theoretic approach to time-inconsistent problems are [2,15,16,17] where PDE methods for specific time-inconsistent problems -that are similar to the general method relying on the extended HJB system of [6,7] -are developed. Recent publications that use different versions of the extended HJB system to study time-inconsistent stochastic control problems include [4,8,9,19,23,25,26,27,35]. In [14], the equilibrium of a time-inconsistent control problem is characterized by a stochastic maximum principle.…”

Section: Introductionmentioning

confidence: 99%

A regular equilibrium solves the extended HJB system

Lindensjö

2019

Operations Research Letters

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Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A fundamental result of time-inconsistent stochastic control is a verification theorem saying that solving the extended HJB system is a sufficient condition for equilibrium. We show that solving the extended HJB system is a necessary condition for equilibrium, under regularity assumptions. The controlled process is a general Itô diffusion. AMS MSC2010: 49J20; 49N90; 93E20; 35Q91; 49L99; 91B51; 91G80.

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