Optimal Investment with Lumpy Adjustment Costs Under Complete Irreversibility: A Tractable Solution in Continuous Time

2011 ◽  
Author(s):  
Hjalte Nerdrum
Keyword(s):  
Continuous Time ◽  
Adjustment Costs ◽  
Optimal Investment

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are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.

A FINITE-HORIZON OPTIMAL INVESTMENT AND CONSUMPTION PROBLEM USING REGIME-SWITCHING MODELS

2014 ◽  
Vol 17 (04) ◽  
pp. 1450027 ◽  
Author(s):  
R. H. LIU
Keyword(s):  
Continuous Time ◽  
Regime Switching ◽  
Optimal Investment ◽  
Finite Horizon ◽  
Power Utility ◽  
Verification Theorem ◽  
Regime Switching Models ◽  
Switching Models ◽  
The Impact ◽  
Optimal Investment And Consumption

This paper is concerned with a finite-horizon optimal investment and consumption problem in continuous-time regime-switching models. The market consists of one bond and n ≥ 1 correlated stocks. An investor distributes his/her wealth among these assets and consumes at a non-negative rate. The market parameters (the interest rate, the appreciation rates and the volatilities of the stocks) and the utility functions are assumed to depend on a continuous-time Markov chain with a finite number of states. The objective is to maximize the expected discounted total utility of consumption and the expected discounted utility from terminal wealth. We solve the optimization problem by applying the stochastic control methods to regime-switching models. Under suitable conditions, we prove a verification theorem. We then apply the verification theorem to a power utility function and obtain, up to the solution of a system of coupled ordinary differential equations, an explicit solution of the value function and the optimal investment and consumption policies. We illustrate the impact of regime-switching on the optimal investment and consumption policies with numerical results and compare the results with the classical Merton problem that has only a single regime.

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 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.

Sign in / Sign up

Export Citation Format

Share Document