Optimal investment and consumption problems under correlation ambiguity

2019 ◽  
Vol 31 (1) ◽  
pp. 69-89 ◽  
Author(s):  
Bingyan Han ◽  
Hoi Ying Wong
Keyword(s):  
Utility Maximization ◽  
Infinite Horizon ◽  
Optimal Investment ◽  
Problem Formulation ◽  
Defined Contribution ◽  
Case Scenario ◽  
Worst Case ◽  
Optimal Decisions ◽  
Expected Utility Maximization ◽  
Optimal Investment And Consumption

Abstract Consider an economy with $d$ stochastic factors that have an ambiguous variance–covariance matrix. An ambiguity- and risk-averse agent seeks to determine the optimal investment and consumption strategy that is robust to the uncertainty in the covariances. We formulate the robust decision rule as an expected utility maximization over the worst-case scenario with respect to all possible covariances. As this variance–covariance ambiguity leads to robust optimal decisions over a set of non-equivalent probability measures, the $G$-expectation framework is adopted to characterize the problem as a maximin optimization. Our problem formulation can be applied to finite and infinite horizon investment–consumption problems with or without a subsistence consumption constraint. We demonstrate our models using two examples including the defined contribution pension problem and lifetime optimal investment–consumption problems.

scholarly journals MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

2015 ◽  
Vol 18 (08) ◽  
pp. 1550053 ◽  
Author(s):  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ETIENNE CHEVALIER ◽  
IDRIS KHARROUBI ◽  
THOMAS LIM
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Worst Case ◽  
Variable Annuities ◽  
Minimization Problems ◽  
Optimal Investment Strategy ◽  
Utility Indifference

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

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 Kim and Omberg Revisited: The Duality Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Anna Battauz ◽  
Marzia De Donno ◽  
Alessandro Sbuelz
Keyword(s):  
Expected Utility ◽  
Explicit Solution ◽  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Maximization Problem ◽  
Expected Utility Maximization ◽  
Duality Approach ◽  
Utility Maximization Problem ◽  
Optimal Investment Problem

We give an alternative duality-based proof to the solution of the expected utility maximization problem analyzed by Kim and Omberg. In so doing, we also provide an example of incomplete-market optimal investment problem for which the duality approach is conducive to an explicit solution.

scholarly journals Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Xiangbo Meng ◽  
Ximin Rong ◽  
Lidong Zhang ◽  
Ziping Du
Keyword(s):  
Model Uncertainty ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Model Parameters ◽  
Case Scenario ◽  
Worst Case ◽  
New Business ◽  
Hamilton Jacobi Bellman ◽  
Quadratic Distance ◽  
The Impact

In this paper, we study optimal investment-reinsurance strategies for an insurer who faces model uncertainty. The insurer is allowed to acquire new business and invest into a financial market which consists of one risk-free asset and one risky asset whose price process is modeled by a Geometric Brownian motion. Minimizing the expected quadratic distance of the terminal wealth to a given benchmark under the “worst-case” scenario, we obtain the closed-form expressions of optimal strategies and the corresponding value function by solving the Hamilton-Jacobi-Bellman (HJB) equation. Numerical examples are presented to show the impact of model parameters on the optimal strategies.

Reducing Probabilistic Weather Forecasts to the Worst Case Scenario: Anchoring Effects

2008 ◽  
Author(s):  
Sonia Savelli ◽  
Susan Joslyn ◽  
Limor Nadav-Greenberg ◽  
Queena Chen
Keyword(s):  
Case Scenario ◽  
Worst Case ◽  
Weather Forecasts ◽  
Worst Case Scenario ◽  
Anchoring Effects

EXPEDITION TO MALI, 2020

2020 ◽  
pp. 12-28
Author(s):  
D. V. Vaniukova ◽  
◽  
P. A. Kutsenkov ◽  
Keyword(s):  
Mass Murder ◽  
The State ◽  
Case Scenario ◽  
Worst Case ◽  
Traditional Art ◽  
Peter The Great ◽  
State Museum ◽  
Bobo Dioulasso ◽  
Oriental Studies ◽  
The Village

The research expedition of the Institute of Oriental studies of the Russian Academy of Sciences has been working in Mali since 2015. Since 2017, it has been attended by employees of the State Museum of the East. The task of the expedition is to study the transformation of traditional Dogon culture in the context of globalization, as well as to collect ethnographic information (life, customs, features of the traditional social and political structure); to collect oral historical legends; to study the history, existence, and transformation of artistic tradition in the villages of the Dogon Country in modern conditions; collecting items of Ethnography and art to add to the collection of the African collection of the. Peter the Great Museum (Kunstkamera, Saint Petersburg) and the State Museum of Oriental Arts (Moscow). The plan of the expedition in January 2020 included additional items, namely, the study of the functioning of the antique market in Mali (the “path” of things from villages to cities, which is important for attributing works of traditional art). The geography of our research was significantly expanded to the regions of Sikasso and Koulikoro in Mali, as well as to the city of Bobo-Dioulasso and its surroundings in Burkina Faso, which is related to the study of migrations to the Bandiagara Highlands. In addition, the plan of the expedition included organization of a photo exhibition in the Museum of the village of Endé and some educational projects. Unfortunately, after the mass murder in March 2019 in the village of Ogossogou-Pel, where more than one hundred and seventy people were killed, events in the Dogon Country began to develop in the worst-case scenario: The incessant provocations after that revived the old feud between the Pel (Fulbe) pastoralists and the Dogon farmers. So far, this hostility and mutual distrust has not yet developed into a full-scale ethnic conflict, but, unfortunately, such a development now seems quite likely.

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

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