Portfolio Optimization under Solvency Constraints: A Dynamical Approach

Asanga, Sujith; Asimit, Alexandru V.; Badescu, Alexandru; Haberman, Steven

doi:10.1080/10920277.2014.910127

Cited by 8 publications

(25 citation statements)

References 34 publications

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“…The problem is equivalent to the one in [5], but a multi-objective approach is here adopted instead of an -constraint scheme. In the Experimental Section, we will investigate the benefits of this choice.…”

Section: Multi-objective Portfolio Optimization Problems With Solvencmentioning

confidence: 99%

“…Putting this expression into Equation (4), we obtain a Monte Carlo estimate for the conditional value-at-risk, whose convexity is a direct consequence of the convexity property of the European call price with respect to the strike price (for more details, we point the interested reader to [5]). By virtue of the liability log normality, the expected net profit can be written as:…”

Section: Quantile-based Risk Measures and Objective Estimationmentioning

confidence: 99%

“…In order to overcome this drawback, we follow the semi-parametric approach used, for instance, in [5] and assume claim amounts to be modeled with a lognormal distribution. This condition is sufficient in most practical cases to guarantee the convexity of the solvency constraint (a more detailed treatment will be provided in the section where we describe the estimation methods).…”

Section: Multi-objective Portfolio Optimization Problems With Solvencmentioning

confidence: 99%

“…The expectation in Equation (4) is approximated according to [5] by exploiting the log normality of Y and the Black-Scholes call price formula; the result is:…”

Section: Quantile-based Risk Measures and Objective Estimationmentioning

confidence: 99%

“…Similarly, in [4], the capital requirement is minimized on the basis of both a ruin probability constraint and a return-on-capital constraint. A dynamic improvement of this approach is provided in [5], where the portfolio optimization is analyzed under three different solvency regimes.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Kaucic¹,

Daris²

2015

Risks

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In the paper, we introduce a multi-objective scenario-based optimization approach for chance-constrained portfolio selection problems. More specifically, a modified version of the normal constraint method is implemented with a global solver in order to generate a dotted approximation of the Pareto frontier for bi-and tri-objective programming problems. Numerical experiments are carried out on a set of portfolios to be optimized for an EU-based non-life insurance company. Both performance indicators and risk measures are managed as objectives. Results show that this procedure is effective and readily applicable to achieve suitable risk-reward tradeoff analysis.

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Section: Multi-objective Portfolio Optimization Problems With Solvencmentioning

confidence: 99%

Section: Quantile-based Risk Measures and Objective Estimationmentioning

confidence: 99%

Section: Multi-objective Portfolio Optimization Problems With Solvencmentioning

confidence: 99%

“…The expectation in Equation (4) is approximated according to [5] by exploiting the log normality of Y and the Black-Scholes call price formula; the result is:…”

Section: Quantile-based Risk Measures and Objective Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Kaucic¹,

Daris²

2015

Risks

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Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint

et al. 2023

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We present an optimization problem to determine the minimum capital requirement for a non-life insurance company. The optimization problem imposes a non-positive Conditional Value-at-Risk (CVaR) of the insurer’s net loss and a portfolio performance constraint. When expressing the optimization problem in a semiparametric form, we demonstrate its convexity for any integrable random variable representing the insurer’s liability. Furthermore, we prove that the function defining the CVaR constraint in the semiparametric formulation is continuously differentiable when the insurer’s liability has a continuous distribution. We use the Kelley-Cheney-Goldstein algorithm to solve the optimization problem in the semiparametric form and show its convergence. An empirical analysis is carried out by assuming three different liability distributions: a lognormal distribution, a gamma distribution, and a mixture of Erlang distributions with a common scale parameter. The numerical experiments show that the choice of the liability distribution plays a crucial role since marked differences emerge when comparing the mixture distribution with the other two distributions. In particular, the mixture distribution describes better the right tail of the empirical distribution of liabilities with respect to the other two distributions and implies higher capital requirements and different assets in the optimal portfolios.

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A multistage stochastic programming asset-liability management model: an application to the Brazilian pension fund industry

et al. 2016

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This paper proposes a multistage stochastic programming approach for the asset-liability management of Brazilian pension funds. We generate asset price scenarios with stochastic differential equations-Geometric Brownian Motion model for stocks and Cox-Ingersoll-Ross model for fixed income securities. Intertemporal solvency regulatory rules for Brazilian pension funds are considered endogenously in the model and enforced with a combinatorial constraint. A VaR probabilistic constraint is incorporated to obtain a positive funding ratio at each time period with high probability. Our approach uses multiple trees to provide a representative characterization of the uncertainty and is not computationally prohibitive. We evaluate the insolvency probability under different initial funding ratios through extensive simulations. The study reveals that the likely decrease of interest rate premiums in the next years will force pension fund managers to significantly change their portfolio strategies. They will have to take more risk in order to deliver the cash flows required to cover the liabilities and satisfy the regulatory constraints.

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Portfolio Optimization under Solvency Constraints: A Dynamical Approach

Cited by 8 publications

References 34 publications

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint

A multistage stochastic programming asset-liability management model: an application to the Brazilian pension fund industry

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