scholarly journals Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hidekazu Yoshioka ◽  
Yuta Yaegashi
Keyword(s):  
Impulse Control ◽  
Bird Population ◽  
Optimal Intervention ◽  
Stochastic Impulse Control ◽  
Quasi Variational Inequality ◽  
Non Local ◽  
Intervention Policy ◽  
Hamilton Jacobi Bellman ◽  
The Many ◽  
The Value Function

AbstractA stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.

scholarly journals Continuity of the value function for deterministic optimal impulse control with terminal state constraint

2021 ◽  
Author(s):  
Yue Zhou ◽  
Xinwei Feng ◽  
Jiongmin Yong
Keyword(s):  
Viscosity Solution ◽  
Impulse Control ◽  
Value Function ◽  
State Constraint ◽  
Terminal State ◽  
Dynamic Programming Principle ◽  
Hamilton Jacobi Bellman ◽  
Optimal Impulse ◽  
The Value Function ◽  
Terminal State Constraint

Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is the introduction of an intrinsic condition under which the value function is proved to be continuous. Then by a Bellman dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman type quasi-variational inequality (QVI, for short) is derived. The value function is proved to be a viscosity solution to such a QVI. The issue of whether the value function is characterized as the unique viscosity solution to this QVI is carefully addressed and the answer is left open challengingly.

scholarly journals A Theory of Foreign Exchange Interventions

2021 ◽  
Author(s):  
Sebastián Fanelli ◽  
Ludwig Straub
Keyword(s):  
Exchange Rate ◽  
Central Bank ◽  
Interest Rates ◽  
Open Economy ◽  
Small Open Economy ◽  
Bond Markets ◽  
Pecuniary Externality ◽  
Optimal Intervention ◽  
The Exchange Rate ◽  
Intervention Policy

Abstract We study a real small open economy with two key ingredients (1) partial segmentation of home and foreign bond markets and (2) a pecuniary externality that makes the real exchange rate excessively volatile in response to capital flows. Partial segmentation implies that, by intervening in the bond markets, the central bank can affect the exchange rate and the spread between home- and foreign-bond yields. Such interventions allow the central bank to address the pecuniary externality, but they are also costly, as foreigners make carry trade profits. We analytically characterize the optimal intervention policy that solves this trade-off: (1) the optimal policy leans against the wind, stabilizing the exchange rate; (2) it involves smooth spreads but allows exchange rates to jump; (3) it partly relies on “forward guidance,” with non-zero interventions even after the shock has subsided; (4) it requires credibility, in that central banks do not intervene without commitment. Finally, we shed light on the global consequences of widespread interventions, using a multi-country extension of our model. We find that, left to themselves, countries over-accumulate reserves, reducing welfare and leading to inefficiently low world interest rates.

scholarly journals Optimal Portfolios for Financial Markets with Wishart Volatility

2013 ◽  
Vol 50 (4) ◽  
pp. 1025-1043 ◽  
Author(s):  
Nicole Bäuerle ◽  
Zejing Li
Keyword(s):  
Value Function ◽  
Numerical Study ◽  
Heston Model ◽  
Hard Part ◽  
Control Approach ◽  
Portfolio Strategy ◽  
Hamilton Jacobi Bellman ◽  
The One ◽  
Hedging Demand ◽  
The Value Function

We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain, explicitly, the optimal portfolio strategy and the value function in some parameter settings. In particular, we do this when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is to identify when the solution of the Hamilton-Jacobi-Bellman equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.

scholarly journals Prediction and prevention of disproportionally dominant agents in complex networks

2020 ◽  
Vol 117 (44) ◽  
pp. 27090-27095
Author(s):  
Sandro Claudio Lera ◽  
Alex Pentland ◽  
Didier Sornette
Keyword(s):  
Complex Networks ◽  
Critical Mass ◽  
Stable State ◽  
Warning System ◽  
Interacting Agents ◽  
Optimal Intervention ◽  
Prediction And Prevention ◽  
The Common ◽  
Intervention Policy ◽  
Winner Takes All

We develop an early warning system and subsequent optimal intervention policy to avoid the formation of disproportional dominance (“winner takes all,” WTA) in growing complex networks. This is modeled as a system of interacting agents, whereby the rate at which an agent establishes connections to others is proportional to its already existing number of connections and its intrinsic fitness. We derive an exact four-dimensional phase diagram that separates the growing system into two regimes: one where the “fit get richer” and one where, eventually, the WTA. By calibrating the system’s parameters with maximum likelihood, its distance from the unfavorable WTA regime can be monitored in real time. This is demonstrated by applying the theory to the eToro social trading platform where users mimic each other’s trades. If the system state is within or close to the WTA regime, we show how to efficiently control the system back into a more stable state along a geodesic path in the space of fitness distributions. It turns out that the common measure of penalizing the most dominant agents does not solve sustainably the problem of drastic inequity. Instead, interventions that first create a critical mass of high-fitness individuals followed by pushing the relatively low-fitness individuals upward is the best way to avoid swelling inequity and escalating fragility.

scholarly journals Stochastic Impulse Control of Non-Markovian Processes

2009 ◽  
Vol 61 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Boualem Djehiche ◽  
Said Hamadène ◽  
Ibtissam Hdhiri
Keyword(s):  
Impulse Control ◽  
Markovian Processes ◽  
Stochastic Impulse Control
Sign in / Sign up

Export Citation Format

Share Document