scholarly journals Optimal investment strategies for pension funds with regulation-conform dynamic pension payment management in the absence of guarantees

2021 ◽  
Author(s):  
Andreas Lichtenstern ◽  
Rudi Zagst
Keyword(s):  
Continuous Time ◽  
Optimization Problem ◽  
Wealth Distribution ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Cash Flows ◽  
Iteration Algorithm ◽  
Coverage Ratio ◽  
Proposed Model ◽  
Bellman Principle

AbstractIn this article we consider the post-retirement phase optimization problem for a specific pension product in Germany that comes without guarantees. The continuous-time optimization problem is defined consisting of two specialties: first, we have a product-specific pension adjustment mechanism based on a certain capital coverage ratio which stipulates compulsory pension adjustments if the pension fund is underfunded or significantly overfunded. Second, due to the retiree’s fear of and aversion against pension reductions, we introduce a total wealth distribution to an investment portfolio and a buffer portfolio to lower the probability of future potential pension shortenings. The target functional in the optimization, that is to be maximized, is the client’s expected accumulated utility from the stochastic future pension cash flows. The optimization outcome is the optimal investment strategy in the proposed model. Due to the inherent complexity of the continuous-time framework, the discrete-time version of the optimization problem is considered and solved via the Bellman principle. In addition, for computational reasons, a policy function iteration algorithm is introduced to find a stationary solution to the problem in a computationally efficient and elegant fashion. A numerical case study on optimization and simulation completes the work with highlighting the benefits of the proposed model.

scholarly journals MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

2015 ◽  
Vol 18 (08) ◽  
pp. 1550053 ◽  
Author(s):  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ETIENNE CHEVALIER ◽  
IDRIS KHARROUBI ◽  
THOMAS LIM
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Worst Case ◽  
Variable Annuities ◽  
Minimization Problems ◽  
Optimal Investment Strategy ◽  
Utility Indifference

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

scholarly journals Optimal Investment Strategy for Risky Assets

1998 ◽  
Vol 01 (03) ◽  
pp. 377-387 ◽  
Author(s):  
Sergei Maslov ◽  
Yi-Cheng Zhang
Keyword(s):  
Growth Rate ◽  
Brownian Motion ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Assets ◽  
Average Return ◽  
Optimal Investment Strategy

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.

scholarly journals A Model for the Optimal Investment Strategy in the Context of Pandemic Regional Lockdown

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1058
Author(s):  
Antoine Tonnoir ◽  
Ioana Ciotir ◽  
Adrian-Liviu Scutariu ◽  
Octavian Dospinescu
Keyword(s):  
Mathematical Model ◽  
Negative Impact ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Economic Consequences ◽  
Decision Makers ◽  
Investment Strategies ◽  
Negative Consequences ◽  
Optimal Investment Strategy ◽  
Proposed Model

The Covid-19 pandemic has generated major changes in society, most of them having a negative impact on the quality of life and income obtained by the population and businesses. The negative consequences have been highlighted in the decrease of the GPD level for regions, countries and even continents. Returning to pre-pandemic levels is a considerable effort for both economic and political decision-makers. This article deals with the construction of a mathematical model for economic aspects in the context of variable productivity in time. Through this mathematical model, we propose to maximize revenues in pandemic conditions, in order to limit the economic consequences of the lockdown. One advantage of the proposed model consists in the fact that it is based on units that can be regions, economic branches, economic units or fields of investment. Another strength of the model is determined by the fact that it offers the possibility to choose between two different investment strategies, based on the specific options of the decision makers: the consistent increase of the state revenues or the amelioration of the disparity phenomenon. Furthermore, our model extends previous approaches from the literature by adding some generalization options and the proposed model can be applied in lockdown cases and seasonal situations.

scholarly journals Optimal investment strategies in a CIR framework

2000 ◽  
Vol 37 (4) ◽  
pp. 936-946 ◽  
Author(s):  
Griselda Deelstra ◽  
Martino Grasselli ◽  
Pierre-François Koehl
Keyword(s):  
Financial Markets ◽  
Interest Rates ◽  
Utility Function ◽  
Closed Form ◽  
Continuous Time ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Optimal Investment Problem

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

scholarly journals Optimal investment strategies in a CIR framework

2000 ◽  
Vol 37 (04) ◽  
pp. 936-946 ◽  
Author(s):  
Griselda Deelstra ◽  
Martino Grasselli ◽  
Pierre-François Koehl
Keyword(s):  
Financial Markets ◽  
Interest Rates ◽  
Utility Function ◽  
Closed Form ◽  
Continuous Time ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Optimal Investment Problem

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

scholarly journals Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 857 ◽  
Author(s):  
Helu Xiao ◽  
Tiantian Ren ◽  
Yanfei Bai ◽  
Zhongbao Zhou
Keyword(s):  
Optimization Problem ◽  
Continuous Process ◽  
Optimal Investment ◽  
Decision Makers ◽  
Weighted Sum ◽  
Proposed Model ◽  
Generalized Mean ◽  
Continuous Trading ◽  
The Impact ◽  
Mean Variance

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

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