Related papers: On the shortfall risk control -- a refinement of t…
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write…
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the…
In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…
We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
Motivated by the analysis of a general optimal portfolio selection problem, which encompasses as special cases an optimal consumption and an optimal debt-arrangement problem, we are concerned with the questions of how a personality trait…
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…
This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the…
We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor's risk and consumption preferences are given as inputs to the neural network in addition to…
We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon $T$ in an incomplete market model, and then study the asymptotic behavior of minimizing probability as $T\to\infty$.…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can…
We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the…