Time-Consistent Investment Strategy with Only Risky Assets and Its Link with Myopic Strategy in High Dimensions

2017 ◽  
Author(s):  
Chi Seng Pun
Keyword(s):  
Investment Strategy ◽  
High Dimensions ◽  
Risky Assets ◽  
Myopic Strategy

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

scholarly journals Constructing an optimal investment portfolio for the Bank of Lithuania

Ekonomika ◽  
2016 ◽  
Vol 95 (1) ◽  
pp. 112-133
Author(s):  
Birutė Galinienė ◽  
Justina Stravinskytė
Keyword(s):  
Management Strategies ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Financial Assets ◽  
Currency Risk ◽  
Investment Portfolio ◽  
Risky Assets ◽  
Course Of Action ◽  
Total State ◽  
Assets Management

The main goal of this article is to illustrate the strategy, devised to improve the effectiveness of utilizing the financial assets, or in this case, the official international reserves, belonging to the Bank of Lithuania. In Lithuania, the value of financial assets as a percentage of total state assets has doubled in the span of 10 years. Moreover, a strong correlation between the real GDP growth and the Bank of Lithuania’s financial assets/profitability implies that the effectiveness of financial assets management has a nationally wide impact. Unfortunately, the Bank’s profit/invested value indicator has reached a record low in 2012–2013, which resulted in the whole bank’s profit being absorbed into the state’s budget (as opposed to 70 % of it). Such signs meant that the previous investment strategy has become ineffective and needed changes.To highlight the necessary changes, the authors conduct a practical research and construct the optimal investment portfolio, according to the goals and variables given by the guidelines, proposed by Bank of Lithuania. The size of the portfolio is 4,14 bn euros, and the maximum loss per year (VaR) allowed is -100 M euro/year, as stated by the Bank of Lithuania’s risk budget limit. The authors also focus on the issue of increased currency risk after investing in volatile share indices and whether hedging against it with Forex spot transactions is beneficial.The result of the research is an optimal portfolio, consisting of 9,85 percent of risk-free assets and 90,15 percent of risky assets. Hedging against currency risk in this case is an ultimately beneficial course of action, yielding an increase of annual returns by 0,3 percent, which translates to +12,3 mln euros. Finally, the portfolio is flexible and simple to reshape into a less risky variant, if the institution predicts the dangers of possible future economic downfalls.This research was further used in a broader paper whose goal was to analyse and assess the effectiveness of currently employed assets’ management strategies in Lithuania.

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.

scholarly journals A conservative discontinuous target volatility strategy

2017 ◽  
Vol 14 (2) ◽  
pp. 176-190 ◽  
Author(s):  
Simone Cirelli ◽  
Sebastiano Vitali ◽  
Sergio Ortobelli Lozza ◽  
Vittorio Moriggia
Keyword(s):  
Standard Deviation ◽  
Asset Management ◽  
Risk Measure ◽  
Investment Strategy ◽  
Time Span ◽  
Portfolio Performance ◽  
Risky Assets ◽  
High Volatility ◽  
Over Time ◽  
Better Than

The asset management sector is constantly looking for a reliable investment strategy, which is able to keep its promises. One of the most used approaches is the target volatility strategy that combines a risky asset with a risk-free trying to maintain the portfolio volatility constant over time. Several analyses highlight that such target is fulfilled on average, but in periods of crisis, the portfolio still suffers market’s turmoils. In this paper, the authors introduce an innovative target volatility strategy: the discontinuous target volatility. Such approach turns out to be more conservative in high volatility periods. Moreover, the authors compare the adoption of the VIX Index as a risk measure instead of the classical standard deviation and show whether the former is better than the latter. In the last section, the authors also extend the analysis to remove the risk-free assumption and to include the correlation structure between two risky assets. Empirical results on a wide time span show the capability of the new proposed strategy to enhance the portfolio performance in terms of standard measures and according to stochastic dominance theory.

Worst-Case Investment Strategy with Delay

2018 ◽  
Vol 6 (1) ◽  
pp. 35-57
Author(s):  
Chunxiang A ◽  
Yi Shao
Keyword(s):  
Financial Market ◽  
Normal State ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Investment Strategies ◽  
Case Scenario ◽  
Worst Case ◽  
Risky Assets ◽  
Investment Optimization

AbstractThis paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

scholarly journals Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Zhongbao Zhou ◽  
Xianghui Liu ◽  
Helu Xiao ◽  
TianTian Ren ◽  
Wenbin Liu
Keyword(s):  
Empirical Studies ◽  
Lagrange Function ◽  
Investment Strategy ◽  
Open Loop ◽  
Investment Strategies ◽  
Variance Model ◽  
Risky Assets ◽  
Consistent Solution ◽  
Mean Variance Portfolio ◽  
Mean Variance

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

scholarly journals Long-Run Savings and Investment Strategy Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Russell Gerrard ◽  
Montserrat Guillén ◽  
Jens Perch Nielsen ◽  
Ana M. Pérez-Marín
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Investment Strategy ◽  
Maximum Amount ◽  
Constant Amount ◽  
Investment Performance ◽  
Risky Assets ◽  
Absolute Risk Aversion ◽  
Long Run ◽  
Life Cycle Savings

We focus on automatic strategies to optimize life cycle savings and investment. Classical optimal savings theory establishes that, given the level of risk aversion, a saver would keep the same relative amount invested in risky assets at any given time. We show that, when optimizing lifecycle investment, performance and risk assessment have to take into account the investor’s risk aversion and the maximum amount the investor could lose, simultaneously. When risk aversion and maximum possible loss are considered jointly, an optimal savings strategy is obtained, which follows from constant rather than relative absolute risk aversion. This result is fundamental to prove that if risk aversion and the maximum possible loss are both high, then holding a constant amount invested in the risky asset is optimal for a standard lifetime saving/pension process and outperforms some other simple strategies. Performance comparisons are based on downside risk-adjusted equivalence that is used in our illustration.

scholarly journals On the Stochastic Optimal Control Model of the Investments of Defined Contribution (DC) Pension Funds

2020 ◽  
Vol 24 (2) ◽  
pp. 63-269
Author(s):  
T. Latunde ◽  
O.O. Esan ◽  
J.O. Richard ◽  
D.D. Dare
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problems ◽  
Absolute Risk ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Pension Funds ◽  
Model Parameters ◽  
Defined Contribution ◽  
Risky Assets ◽  
Hamilton Jacobi Bellman

One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. In this work, optimal investment for a stochastic model of a Defined contribution (DC) is investigated such that the model design is analysed yielding an optimized expected utility of the members’ terminal wealth. An optimized solution is derived using the Hamilton Jacobi equation in solving the problem of investment strategy formulated by Constant absolute risk aversion (CARA). However, to consider the changes that occur in the dimension of optimal solutions in optimization problems, mostly, the optimal behaviour of parameters, the sensitivity analysis is considered. Thus, the analysis of the model is carried out herein by utilising the approach of the sensitivity analysis of parameters. This is carried out by using Maple software and varying the values of some model parameters such that the behaviour of each parameter relating to the pension funds invested in the risky assets is determined. The results are presented graphically and using tables thus discussed such that pension investors and stakeholders are advised. Keywords: Stochastic; DC Pension funds; Sensitivity analysis; Hamilton-Jacobi-Bellman equation; Optimal investment

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