1,721,008 research outputs found
Stochastic Differential Games Involving Impulse Controls and Double-Obstacle Quasi-variational Inequalities
No full textWe study a two-player zero-sum stochastic differential game with both players adopt- ing impulse controls, on a finite time horizon. The Hamilton–Jacobi–Bellman–Isaacs (HJBI) partial differential equation (PDE) of the game turns out to be a double-obstacle quasi-variational inequality; therefore the two obstacles are implicitly given. We prove that the upper and lower value functions coincide; indeed we show, by means of the dynamic programming principle for the stochastic differential game, that they are the unique viscosity solution to the HJBI equation, therefore proving that the game admits a value
Backward SDE representation for stochastic control problems with nondominated controlled intensity
Full text linkWe are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problem is associated to a fully nonlinear integro-partial differential equation, which has the peculiarity that the measure (λ(a, ·))a characterizing the jump part is not fixed but depends on a parameter a which lives in a compact set A of some Euclidean space Rq . We do not assume that the family (λ(a, ·))a is dominated. Moreover, the diffusive part can be degenerate. Our aim is to give a BSDE representation, known as a nonlinear Feynman-Kac formula, for the value function associated with these control problems. For this reason, we introduce a class of backward stochastic differential equations with jumps and a partially constrained diffusive part.We look for the minimal solution to this family of BSDEs, for which we prove uniqueness and existence by means of a penalization argument. We then show that the minimal solution to our BSDE provides the unique viscosity solution to our fully nonlinear integro-partial differential equation
A Tikhonov Theorem for McKean–Vlasov Two-Scale Systems and a New Application to Mean Field Optimal Control Problems
Full text linkEquilibrium price in intraday electricity markets
No full textWe formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity. Forecasts are prone to idiosyncratic noise as well as common noise (weather). Agents production capacities are subject to independent random outages, which are each modeled by a Markov chain. The equilibrium price is defined as the price that minimizes trading cost plus imbalance cost of each agent and satisfies the usual market clearing condition. Existence and uniqueness of the equilibrium are proved, and we show that the equilibrium price and the optimal trading strategies are martingales. The main economic insights are the following. (i) When there is no uncertainty on generation, it is shown that the market price is a convex combination of forecasted marginal cost of each agent, with deterministic weights. Furthermore, the equilibrium market price is consistent with Almgren and Chriss's model and we identify the fundamental part as well as the permanent market impact. It turns out that heterogeneity across agents is a necessary condition for Samuelson's effect to hold. We show that when heterogeneity lies only on costs, Samuelson's effect holds true. A similar result stands when heterogeneity lies only on market access quality. (ii) When there is production uncertainty only, we provide an approximation of the equilibrium for large number of players. The resulting price exhibits increasing volatility with time
American option valuation in a stochastic volatility model with transaction costs
Full text linkIn the present paper we analyse the American option valuation problem in a stochastic volatility model when transaction costs are taken into account. We shall show that it can be formulated as a singular stochastic optimal control problem, proving the existence and uniqueness of the viscosity solution for the associated Hamilton-Jacobi-Bellman partial differential equation. Moreover, after performing a dimensionality reduction through a suitable choice of the utility function, we shall provide a numerical example illustrating how American options prices can be computed in the present modelling framework
Optimal control of path-dependent McKean-Vlasov SDEs in infinite dimension
Full text linkWe study the optimal control of path-dependent McKean-Vlasov equations valued
in Hilbert spaces motivated by non Markovian mean-field models driven by
stochastic PDEs. We first establish the well-posedness of the state equation,
and then we prove the dynamic programming principle (DPP) in such a general
framework. The crucial law invariance property of the value function V is
rigorously obtained, which means that V can be viewed as a function on the
Wasserstein space of probability measures on the set of continuous functions
valued in Hilbert space. We then define a notion of pathwise measure
derivative, which extends the Wasserstein derivative due to Lions [41], and
prove a related functional It{\^o} formula in the spirit of Dupire [24] and Wu
and Zhang [51]. The Master Bellman equation is derived from the DPP by means of
a suitable notion of viscosity solution. We provide different formulations and
simplifications of such a Bellman equation notably in the special case when
there is no dependence on the law of the control.Comment: 54 page
Portfolio choices and VaR constraint with a defaultable asset
No full textWe consider a Constant Elasticity of Variance (CEV) model for the asset price of a defaultable asset showing the so-called leverage effect (high volatility when the asset price is low). We show that a VaR constraint re-evaluated over time induces an agent more risk averse than a logarithmic utility to take more risk than in the unconstrained setting
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
No full textWe study a stochastic optimal control problem for a partially observed diffusion. By using the
control randomization method in Bandini et al. (2018), we prove a corresponding randomized dynamic
programming principle (DPP) for the value function, which is obtained from a flow property of an associated
filter process. This DPP is the key step towards our main result: a characterization of the value function
of the partial observation control problem as the unique viscosity solution to the corresponding dynamic
programming Hamilton–Jacobi–Bellman (HJB) equation. The latter is formulated as a new, fully non linear
partial differential equation on the Wasserstein space of probability measures. An important feature of
our approach is that it does not require any non-degeneracy condition on the diffusion coefficient, and no
condition is imposed to guarantee existence of a density for the filter process solution to the controlled
Zakai equation. Finally, we give an explicit solution to our HJB equation in the case of a partially observed
non Gaussian linear–quadratic model
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