Optimal investment for an insurer with cointegrated assets: CRRA utility

Chiu, Mei Choi; Wong, Hoi Ying

doi:10.1016/j.insmatheco.2012.11.004

Cited by 27 publications

(20 citation statements)

References 21 publications

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“…Although they successfully solve the problem for the case of a single mean-reverting risky asset and a risk-free bond, their solution can be generalized only to uncorrelated cointegrated assets. Liu and Timmermann [12] 1 and Chiu and Wong [13] consider optimal investment problems with cointegrated asset by maximizing the constant relative risk aversion (CRRA) utility function for a hedge fund and insurer, respectively. Both of them assume that cointegration implies statistical arbitrage.…”

Section: Introductionmentioning

confidence: 99%

Dynamic cointegrated pairs trading: Mean–variance time-consistent strategies

Chiu¹,

Wong

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tCointegration is a useful econometric tool for identifying assets which share a common equilibrium. Cointegrated pairs trading is a trading strategy which attempts to take a profit when cointegrated assets depart from their equilibrium. This paper investigates the optimal dynamic trading of cointegrated assets using the classical mean-variance portfolio selection criterion. To ensure rational economic decisions, the optimal strategy is obtained over the set of time-consistent policies from which the optimization problem is enforced to obey the dynamic programming principle. We solve the optimal dynamic trading strategy in a closed-form explicit solution from a nonlinear Hamilton-Jacobi-Bellman partial differential equation. This analytical tractability enables us to prove rigorously that cointegration ensures the existence of statistical arbitrage using a dynamic time-consistent mean-variance strategy via asymptotic analysis. This provides the theoretical grounds for the market belief in cointegrated pairs trading. Comparison between time-consistent and precommitment trading strategies for cointegrated assets shows the former to be a persistent approach, whereas the latter makes it possible to generate infinite leverage once a cointegrating factor of the assets has a high mean reversion rate.

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Section: Introductionmentioning

confidence: 99%

Dynamic cointegrated pairs trading: Mean–variance time-consistent strategies

Chiu¹,

Wong

2015

Journal of Computational and Applied Mathematics

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“…This kind of stochastic model is not considered in the utility maximization problem nor in the insurance literature, to the best of our knowledge. It is shown in [8][9][10] that optimal investment associated with jump-diffusion models could be challenging mathematical problems. The problem considered in the present paper even adds the stochastic interest rate.…”

Section: Introductionmentioning

confidence: 99%

“…While solving the PIDE is the first challenge, proving the verification theorem for the solution of the PIDE being the eligible optimal value function is another. The verification theorem is deduced using the recent framework of Chiu and Wong [10] when there is a mean-reverting stochastic variable, which is the interest rate in our case.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment for Insurers with the Extended CIR Interest Rate Model

Chiu

Wong

2014

Abstract and Applied Analysis

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A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

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“…Most of the publications focus on classic portfolio selection problems and extend previous models. Chiu and Wong () are concerned with the optimal investment behavior of insurers when cointegrated assets are present and insurers are subject to random claims payments. The availability of cointegrated risky assets implies the potential presence of arbitrage opportunities.…”

Section: Resultsmentioning

confidence: 99%

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

Biener

Eling

2013

Risk Manage Insurance Review

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This article reports the main results of the 2012 Risk Premium Project update, a yearly review of actuarial and finance literature on the theory and empirics of risk assessment for property-casualty insurance. Pricing and modeling insurance risks and methodological advancement in risk valuation were popular fields of research in 2012. Of special note is new work on behavioral pricing and liquidity. Additionally, underwriting cycles attracted some controversy, and emerging risks, such as systemic risk and potential interrelations between insurance and other financial markets, were also areas of intense discussion.

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Optimal investment for an insurer with cointegrated assets: CRRA utility

Cited by 27 publications

References 21 publications

Dynamic cointegrated pairs trading: Mean–variance time-consistent strategies

Dynamic cointegrated pairs trading: Mean–variance time-consistent strategies

Optimal Investment for Insurers with the Extended CIR Interest Rate Model

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update

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