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.

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.

scholarly journals On properties of one functional used in software constructions for solving differential games

2021 ◽  
Vol 31 (4) ◽  
pp. 668-696
Author(s):  
A.G. Chentsov
Keyword(s):  
Value Function ◽  
Sufficient Conditions ◽  
Game Problem ◽  
Limit Function ◽  
Phase Constraints ◽  
Nonlinear Differential Game ◽  
Target Set ◽  
Iteration Number ◽  
Game Position ◽  
The Value Function

Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.

The value function for time-related decisions

2011 ◽  
Author(s):  
Anouk Festjens ◽  
Siegfried Dewitte ◽  
Enrico Diecidue ◽  
Sabrina Bruyneel
Keyword(s):  
Value Function ◽  
The Value Function

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

scholarly journals Robo-Advising: Learning Investors’ Risk Preferences via Portfolio Choices*

2020 ◽  
Author(s):  
Humoud Alsabah ◽  
Agostino Capponi ◽  
Octavio Ruiz Lacedelli ◽  
Matt Stern
Keyword(s):  
Opportunity Cost ◽  
Value Function ◽  
Risk Preference ◽  
Portfolio Decisions ◽  
Learning Framework ◽  
Portfolio Choices ◽  
Trading Decisions ◽  
Exploration Exploitation ◽  
The Value Function ◽  
Over Time

Abstract We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor’s risk preference but learns it over time by observing her portfolio choices in different market environments. We develop an exploration–exploitation algorithm that trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor’s risk aversion. We show that the approximate value function constructed by the algorithm converges to the value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor’s mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor’s opportunity cost for making portfolio decisions.

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