Closed-Form Optimal Investment when Present Values and Costs are Jump-Diffusions

2006 ◽  
Author(s):  
Alessandro Sbuelz ◽  
Anna Battauz
Keyword(s):  
Closed Form ◽  
Optimal Investment ◽  
Jump Diffusions

A Hilbert transform approach for controlled jump-diffusions with financial applications

2020 ◽  
Vol 07 (04) ◽  
pp. 2050027
Author(s):  
Yingming Ge ◽  
Lingfei Li
Keyword(s):  
Hilbert Transform ◽  
Optimal Investment ◽  
Small Time ◽  
Computational Method ◽  
Computationally Efficient ◽  
Jump Diffusions ◽  
Piecewise Constant ◽  
Time Dynamic ◽  
Financial Applications ◽  
Dynamic Programming Problem

We propose a new computational method for a class of controlled jump-diffusions for financial applications. In the first step of our method, we apply piecewise constant policy approximation where we partition the time horizon into small time intervals and the control is constant on each interval. In the second step, we develop a Hilbert transform approach to solve a discrete time dynamic programming problem. We provide rigorous error bounds for the piecewise constant policy approximation for controlled jump-diffusions, generalizing previous results for diffusions. We also apply our method to solve two classical types of financial problems: option pricing under uncertain volatility and/or correlation models and optimal investment, including utility maximization and mean-variance portfolio selection. Through various numerical examples, we demonstrate the properties of our method and show that it is a computationally efficient choice for low-dimensional problems. Our method also compares favorably with some popular approaches.

scholarly journals Global Closed-Form Approximation of Free Boundary for Optimal Investment Stopping Problems

2019 ◽  
Vol 57 (3) ◽  
pp. 2092-2121
Author(s):  
Jingtang Ma ◽  
Jie Xing ◽  
Harry Zheng
Keyword(s):  
Free Boundary ◽  
Closed Form ◽  
Optimal Investment ◽  
Closed Form Approximation

scholarly journals Optimal Investment of DC Pension Plan under Incentive Schemes and Loss Aversion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yinghui Dong ◽  
Wenxin Lv ◽  
Siyuan Wei ◽  
Yeyang Gong
Keyword(s):  
Closed Form ◽  
Loss Aversion ◽  
Pension Plan ◽  
Optimal Investment ◽  
Numerical Results ◽  
Managerial Compensation ◽  
Incentive Schemes ◽  
Terminal Wealth ◽  
Portfolio Problem ◽  
Form Representation

We investigate the DC pension manager’s portfolio problem when the manager is remunerated through two schemes for DC pension managerial compensation under loss aversion and minimum guarantee. We apply the concavification technique and a static Lagrangian technique to solve the problem and derive the closed-form representation of the optimal wealth and portfolio processes. Theoretical and numerical results show that the incentive schemes can significantly impact the distribution of the optimal terminal wealth.

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.

ALGORITHMIC TRADING OF CO-INTEGRATED ASSETS

2016 ◽  
Vol 19 (06) ◽  
pp. 1650038 ◽  
Author(s):  
ÁLVARO CARTEA ◽  
SEBASTIAN JAIMUNGAL
Keyword(s):  
Closed Form ◽  
Expected Utility ◽  
Asset Prices ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Algorithmic Trading ◽  
Common Component ◽  
Optimal Investment Strategy

We assume that the drift in the returns of asset prices consists of an idiosyncratic component and a common component given by a co-integration factor. We analyze the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets. The optimal solution is constructed explicitly in closed-form and is shown to be affine in the co-integration factor. We calibrate the model to three assets traded on the Nasdaq exchange (Google, Facebook, and Amazon) and employ simulations to showcase the strategy’s performance.

Estimating jump–diffusions using closed-form likelihood expansions

2016 ◽  
Vol 195 (1) ◽  
pp. 51-70 ◽  
Author(s):  
Chenxu Li ◽  
Dachuan Chen
Keyword(s):  
Closed Form ◽  
Jump Diffusions
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