scholarly journals Sufficient Conditions for the Value Function and Optimal Strategy to be Even and Quasi-Convex

2018 ◽  
Vol 63 (11) ◽  
pp. 3858-3864 ◽  
Author(s):  
Jhelum Chakravorty ◽  
Aditya Mahajan
Keyword(s):  
Optimal Strategy ◽  
Value Function ◽  
Sufficient Conditions ◽  
The Value Function

scholarly journals Optimal capital injections and dividends with tax in a risk model in discrete time

2020 ◽  
Vol 10 (1) ◽  
pp. 235-259
Author(s):  
Katharina Bata ◽  
Hanspeter Schmidli
Keyword(s):  
Discrete Time ◽  
Optimal Strategy ◽  
Bellman Equation ◽  
Value Function ◽  
Risk Model ◽  
Barrier Type ◽  
Optimal Capital ◽  
Capital Injections ◽  
The Value Function ◽  
Special Case

AbstractWe consider a risk model in discrete time with dividends and capital injections. The goal is to maximise the value of a dividend strategy. We show that the optimal strategy is of barrier type. That is, all capital above a certain threshold is paid as dividend. A second problem adds tax to the dividends but an injection leads to an exemption from tax. We show that the value function fulfils a Bellman equation. As a special case, we consider the case of premia of size one. In this case we show that the optimal strategy is a two barrier strategy. That is, there is a barrier if a next dividend of size one can be paid without tax and a barrier if the next dividend of size one will be taxed. In both models, we illustrate the findings by de Finetti’s example.

scholarly journals Optimising dividends and consumption under an exponential CIR as a discount factor

2020 ◽  
Vol 92 (2) ◽  
pp. 285-309
Author(s):  
Julia Eisenberg ◽  
Yuliya Mishura
Keyword(s):  
Brownian Motion ◽  
Optimal Strategy ◽  
Value Function ◽  
Insurance Company ◽  
Parameter Choice ◽  
Surplus Process ◽  
Dividend Payments ◽  
Cir Process ◽  
The Value Function ◽  
Special Parameter

AbstractWe consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we are able to show that for a special parameter choice the optimal strategy is a constant-barrier strategy.

scholarly journals A note on the optimal dividends paid in a foreign currency

2016 ◽  
Vol 11 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Julia Eisenberg ◽  
Paul Krühner
Keyword(s):  
Brownian Motion ◽  
Optimal Strategy ◽  
Value Function ◽  
Foreign Currency ◽  
Initial Capital ◽  
Brownian Motion With Drift ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
The Value Function

AbstractWe consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as a Lévy process. We consider both cases: restricted and unrestricted dividend payments. It turns out that the value function and the optimal strategy can be calculated explicitly.

scholarly journals Optimal Harvesting When the Exchange Rate Is a Semimartingale

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
E. R. Offen ◽  
E. M. Lungu
Keyword(s):  
Exchange Rate ◽  
General Solution ◽  
Value Function ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Singular Stochastic Control ◽  
Total Income ◽  
Black Scholes ◽  
The Exchange Rate ◽  
The Value Function

We consider harvesting in the Black-Scholes Quanto Market when the exchange rate is being modeled by the process Et=E0exp⁡{Xt}, where Xt is a semimartingale, and we ask the following question: What harvesting strategy γ* and the value function Φ maximize the expected total income of an investment? We formulate a singular stochastic control problem and give sufficient conditions for the existence of an optimal strategy. We found that, if the value function is not too sensitive to changes in the prices of the investments, the problem reduces to that of Lungu and Øksendal. However, the general solution of this problem still remains elusive.

Adaptive approach to some stopping problems

1985 ◽  
Vol 22 (3) ◽  
pp. 644-652 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Optimal Strategy ◽  
Value Function ◽  
Secretary Problem ◽  
Adaptive Approach ◽  
Parking Problem ◽  
Monotonicity Properties ◽  
The Value Function

This paper mainly considers the adaptive version of two typical stopping problems, i.e., the parking problem and the secretary problem with refusal. In the first problem, while driving towards a destination, we observe the successive parking places and note whether or not they are occupied. Unoccupied spaces are assumed to occur independently, with probability p. The second problem is to select the best applicant from a population, where each applicant refuses an offer with probability 1 – p. We assume beta prior for p in advance. As time progresses, we update our belief for p in a Bayesian manner based on the observed states of the process. We derive several monotonicity properties of the value function and characterize the optimal strategy in either problem. We also attempt to relax the same probability condition in the classical parking problem.

Adaptive approach to some stopping problems

1985 ◽  
Vol 22 (03) ◽  
pp. 644-652 ◽  
Author(s):  
Mitsushi Tamaki
Keyword(s):  
Optimal Strategy ◽  
Value Function ◽  
Secretary Problem ◽  
Adaptive Approach ◽  
Parking Problem ◽  
Monotonicity Properties ◽  
The Value Function

This paper mainly considers the adaptive version of two typical stopping problems, i.e., the parking problem and the secretary problem with refusal. In the first problem, while driving towards a destination, we observe the successive parking places and note whether or not they are occupied. Unoccupied spaces are assumed to occur independently, with probability p. The second problem is to select the best applicant from a population, where each applicant refuses an offer with probability 1 – p. We assume beta prior for p in advance. As time progresses, we update our belief for p in a Bayesian manner based on the observed states of the process. We derive several monotonicity properties of the value function and characterize the optimal strategy in either problem. We also attempt to relax the same probability condition in the classical parking problem.

scholarly journals TRADING STRATEGIES WITHIN THE EDGES OF NO-ARBITRAGE

2018 ◽  
Vol 21 (03) ◽  
pp. 1850025
Author(s):  
ÁLVARO CARTEA ◽  
SEBASTIAN JAIMUNGAL ◽  
JASON RICCI
Keyword(s):  
Optimal Control ◽  
Optimal Strategy ◽  
Value Function ◽  
Mathematical Framework ◽  
Reflected Brownian Motion ◽  
No Arbitrage ◽  
Limit Orders ◽  
Market Orders ◽  
Bid Ask Spreads ◽  
The Value Function

We develop a trading strategy that employs limit and market orders in a multiasset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the mid-price processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the bid–ask spreads of the assets. We provide a mathematical framework for such an economy and solve for the value function and optimal control for an investor who takes positions in these assets. The optimal strategy exhibits two dominant features which depend on how far the vector of mid-prices is from the no-arbitrage bounds. When mid-prices are sufficiently far from the no-arbitrage edges, the strategy behaves as that of a market maker who posts buy and sell limit orders. And when the mid-price vector is close to the edge of the no-arbitrage region, the strategy executes a combination of market orders and limit orders to profit from statistical arbitrages. We discuss a numerical scheme to solve for the value function and optimal control, and perform a simulation study to discuss the main characteristics of the optimal strategy.

scholarly journals Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited

2006 ◽  
Vol 6 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Thorsten V. Koeppl
Keyword(s):  
Risk Sharing ◽  
Value Function ◽  
Sufficient Conditions ◽  
Efficient Frontier ◽  
Limited Commitment ◽  
History Dependence ◽  
Efficient Allocations ◽  
The Value Function

This paper shows that the value function describing efficient risk sharing with limited commitment is not necessarily differentiable everywhere. We link differentiability of the value function to history dependence of efficient allocations and provide sufficient conditions for both properties.

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