Optimal asset allocation for a bank under risk control

2018 ◽  
Vol 05 (03) ◽  
pp. 1850022 ◽  
Author(s):  
Ryle S. Perera ◽  
Kimitoshi Sato
Keyword(s):  
Asset Allocation ◽  
Control Strategies ◽  
Risk Control ◽  
Closed Form Solution ◽  
Optimal Investment ◽  
Form Solution ◽  
Capital Adequacy ◽  
Stock Index ◽  
Risk Exposure ◽  
Price Dynamics

Motivated by the Basel III requirement we analyze an optimal Capital Adequacy Ratio subject to foreclosure risk exposure. We assume that the banker invests in treasuries, a stock index and a loan portfolio, where he/she wishes to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control strategies. The dynamics of the stock index and the banker’s risk exposure towards foreclosure is modeled as two independent compensated pure jump Lévy Processes. By applying the martingale approach we obtain a closed form solution for this optimization problem under a quadratic utility function. A negative correlation between the banker’s foreclosure risk and the price dynamics of stock index will result in a reduced amount invested in stock index fund while a positive correlation between the banker’s foreclosure risk and the price dynamics of stock index will increase the amount invested in stock index fund.

scholarly journals Optimal Investment for Insurers with the Extended CIR Interest Rate Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Choi Chiu ◽  
Hoi Ying Wong
Keyword(s):  
Interest Rate ◽  
Closed Form Solution ◽  
Critical Factor ◽  
Compound Poisson Process ◽  
Optimal Investment ◽  
Form Solution ◽  
Insurance Companies ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Jump Diffusion Model

A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

scholarly journals Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chubing Zhang
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Pension Funds ◽  
Form Solution ◽  
Defined Contribution ◽  
Time Dynamic ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Dynamic asset allocation for a bank under CRRA and HARA framework

2015 ◽  
Vol 02 (03) ◽  
pp. 1550031 ◽  
Author(s):  
Ryle S. Perera
Keyword(s):  
Interest Rate ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Asset Allocation ◽  
Absolute Risk ◽  
Optimal Investment ◽  
Stock Index ◽  
Investment Horizon ◽  
Power Utility ◽  
Dynamic Portfolio Optimization

This paper analyzes an optimal investment and management strategy for a bank under constant relative risk aversion (CRRA) and hyperbolic absolute risk aversion (HARA) utility functions. We assume that the bank can invest in treasuries, stock index fund and loans, in an environment subject to stochastic interest rate and inflation uncertainty. The interest rate and the expected rate of inflation follow a correlated Ornstein–Uhlenbeck processes and the risk premia are constants. Then we consider the portfolio choice under a power utility that the bank's shareholders can maximize expected utility of wealth at a given investment horizon. Closed form solutions are obtained in a dynamic portfolio optimization model. The results indicate that the optimal proportion invested in treasuries increases while the optimal proportion invested in the loans progressively decreases with respect to time.

Modeling and Control of Surface Quality in Chemical Mechanical Planarization (CMP)

2017 ◽  
Author(s):  
Pavan Poosarla ◽  
Hamid Emadi ◽  
Abhijit Chandra ◽  
Sourabh Bhattacharya
Keyword(s):  
State Space ◽  
Control Strategies ◽  
Chemical Mechanical Planarization ◽  
State Space Model ◽  
Closed Form Solution ◽  
Surface Profile ◽  
Open Loop ◽  
Form Solution ◽  
Machining Process ◽  
Loop Control

Obtaining uniform surface finish across large length scales is extremely important in Chemical Mechanical Planarization (CMP). Existing control strategies use results from model simulations to propose open-loop control strategies to reduce the step height on surfaces being polished. In the present work, we propose a strategy to control the surface profile of substrate during CMP process. The evolution of the surface profile is predicted using the state space model of the polishing process. The resulting state space equation is solved and a closed form solution of the surface profile is obtained as a function of time. Based on the solution, we provide a fundamental limitation for the machining process in terms of the extent of planarization that can be achieved for a given material budget.

Provisions for bank deposit withdrawals and portfolio selection

2020 ◽  
Vol 07 (01) ◽  
pp. 1950037
Author(s):  
Ryle S. Perera
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Form Solution ◽  
Investment Portfolio ◽  
Efficient Manner ◽  
Selection For ◽  
Mean Variance Portfolio ◽  
Mean Variance

The primary economic function of a bank is to redirect funds from savers to borrowers in an efficient manner, while increasing the value of the bank’s asset holdings in absolute terms. Within the regulatory framework of the Basel III accord, banks are required to maintain minimum liquidity to guard against withdrawals/liquidity risks. In this paper, we analyze a continuous-time mean-variance portfolio selection for a bank with stochastic withdrawal provisioning by relating the reserves as a proxy for the assets held by the bank. We then formulate an optimal investment portfolio selection for a banker by constructing a special Riccati equation as a continuous solution to the Hamilton–Jacobi–Bellman (HJB) equation under mean-variance paradigm. We obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of the reserve, depository, and intrinsic risk that are associated with the reserve process.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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