CLOSED-FORM SOLUTIONS FOR OPTIMAL PORTFOLIO SELECTION WITH STOCHASTIC INTEREST RATE AND INVESTMENT CONSTRAINTS

2005 ◽  
Vol 15 (4) ◽  
pp. 539-568 ◽  
Author(s):  
Jér^me Detemple ◽  
Marcel Rindisbacher
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Portfolio Selection ◽  
Optimal Portfolio ◽  
Stochastic Interest Rate ◽  
Closed Form Solutions ◽  
Stochastic Interest ◽  
Optimal Portfolio Selection ◽  
Investment Constraints

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

scholarly journals Optimal dividends in the dual risk model under a stochastic interest rate

2017 ◽  
Vol 04 (01) ◽  
pp. 1750010
Author(s):  
Zailei Cheng
Keyword(s):  
Interest Rate ◽  
Risk Model ◽  
Stochastic Interest Rate ◽  
Closed Form Solutions ◽  
Optimal Dividends ◽  
Optimal Dividend ◽  
Stochastic Interest ◽  
Dual Risk Model ◽  
Optimal Dividend Strategy ◽  
Exponential Lévy Process

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under a stochastic interest rate, assuming the discounting factor follows a geometric Brownian motion or exponential Lévy process. We will show that closed form solutions can be obtained.

scholarly journals Portfolio Strategy for an Investor with Logarithm Utility and Stochastic Interest Rate under Constant Elasticity of Variance Model

2020 ◽  
pp. 186-196
Author(s):  
Edikan E. Akpanibah ◽  
Udeme Ini
Keyword(s):  
Interest Rate ◽  
Optimal Portfolio ◽  
Risky Asset ◽  
Stochastic Interest Rate ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Portfolio Strategy ◽  
Expansion Technique ◽  
Stochastic Interest

This paper is aim at maximizing the expected utility of an investor’s terminal wealth; to achieve this, we study the optimal portfolio strategy for an investor with logarithm utility function under constant elasticity of variance (CEV) model in the presence of stochastic interest rate. A portfolio comprising of one risk free asset and one risky asset is considered where the risk free interest rate follows the Cox- Ingersoll-Ross (CIR) model and the risky asset is modelled by CEV. Using power transformation, change of Variable and asymptotic expansion technique, an explicit solution of the optimal portfolio strategy and the Value function is obtained. Furthermore, numerical simulations are presented to study the effect of some parameters on the optimal portfolio strategy under stochastic interest rate.

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