scholarly journals Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2257
Author(s):  
Julia Eisenberg ◽  
Stefan Kremsner ◽  
Alexander Steinicke
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Interest Rates ◽  
Optimal Control Problems ◽  
Stopping Time ◽  
Maximization Problem ◽  
Control Problems ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
And Behavior

We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve α(t) can be found to determine the optimal strategy at time t. In a second setting, we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach, and we also use backward stochastic differential equations.

scholarly journals Valuing Multirisk Catastrophe Reinsurance Based on the Cox–Ingersoll–Ross (CIR) Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wen Chao
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Threshold Model ◽  
Copula Function ◽  
Dartmouth College ◽  
Insurance Companies ◽  
Stochastic Interest Rates ◽  
Cir Model ◽  
Stochastic Interest ◽  
Catastrophe Reinsurance

Catastrophe risks lead to severe problems of insurance and reinsurance industry. In order to reduce the underwriting risk, the insurer would seek protection by transferring part of its risk exposure to the reinsurer. A framework for valuing multirisk catastrophe reinsurance under stochastic interest rates driven by the CIR model shall be discussed. To evaluate the distribution and the dependence of catastrophe variables, the Peaks over Threshold model and Copula function are used to measure them, respectively. Furthermore, the parameters of the valuing model are estimated and calibrated by using the Global Flood Date provided by Dartmouth College from 2000 to 2016. Finally, the value of catastrophe reinsurance is derived and a sensitivity analysis of how stochastic interest rates and catastrophe dependence affect the values is performed via Monte Carlo simulations. The results obtained show that the catastrophe reinsurance value is the inverse relation between initial value of interest rate and average interest rate in the long run. Additionally, a high level of dependence between catastrophe variables increases the catastrophe reinsurance value. The findings of this paper may be interesting to (re)insurance companies and other financial institutions that want to transfer catastrophic risks.

A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Atsuyuki Kogure ◽  
Takahiro Fushimi
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Longevity Bonds ◽  
Carter Model

AbstractMortality-linked securities such as longevity bonds or longevity swaps usually depend on not only mortality risk but also interest rate risk. However, in the existing pricing methodologies, it is often the case that only the mortality risk is modeled to change in a stochastic manner and the interest rate is kept fixed at a pre-specified level. In order to develop large and liquid longevity markets, it is essential to incorporate the interest rate risk into pricing mortality-linked securities. In this paper we tackle the issue by considering the pricing of longevity derivatives under stochastic interest rates following the CIR model. As for the mortality modeling, we use a two-factor extension of the Lee-Carter model by noting the recent studies which point out the inconsistencies of the original Lee-Carter model with observed mortality rates due to its single factor structure. To address the issue of parameter uncertainty, we propose using a Bayesian methodology both to estimate the models and to price longevity derivatives in line with (Kogure, A., and Y. Kurachi. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.”

scholarly journals Valuing strategic investments under stochastic interest rates: A real option approach

2019 ◽  
Vol 16 (3) ◽  
pp. 89-97
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Davide Radi
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Interest Rates ◽  
Real Option ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Investment Projects ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate

One of the most challenging issues in management is the valuation of strategic investments. In particular, when undertaking projects such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, which are characterized by a long-term horizon, a firm has also to face the risk due to the interest rate. In this work, we propose to value investments subject to interest rate risk using a real options approach (Schulmerich, 2010). This task requires the typical technicalities of option pricing, which often rely on complex and time-consuming techniques to value investment projects. For instance, Schulmerich (2010) is, to the best of our knowledge, the first work where the interest rate risk is considered for real option analysis. Nevertheless, the valuation of investment projects is done by employing binomial trees, which are computationally very expensive. In the current paper, a different modeling framework (in continuous-time) for real option pricing is proposed which allows one to account for interest rate risk and, at the same time, to reduce computational complexity. In particular, the net present value of the cash inflows is specified by a geometric Brownian motion and the interest rate is modeled by using a process of Vasicek type, which is calibrated to real market data. Such an approach yields an explicit formula for valuing various kinds of investment strategies, such as the option to defer and the option to expand. Therefore, the one proposed is the first model in the field of real options that accounts for the interest rate risk and, at the same time, offers an easy to implement formula which makes the model itself very suitable for practitioners. An empirical analysis is presented which illustrates the proposed approach from the practical point-of-view and highlights the impact of stochastic interest rates in investment valuation.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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