Papers by Boualem Djehiche
Risks, 2021
We propose a hybrid classical-quantum approach for modeling transition probabilities in health an... more We propose a hybrid classical-quantum approach for modeling transition probabilities in health and disability insurance. The modeling of logistic disability inception probabilities is formulated as a support vector regression problem. Using a quantum feature map, the data are mapped to quantum states belonging to a quantum feature space, where the associated kernel is determined by the inner product between the quantum states. This quantum kernel can be efficiently estimated on a quantum computer. We conduct experiments on the IBM Yorktown quantum computer, fitting the model to disability inception data from a Swedish insurance company.
Beyond Traditional Probabilistic Methods in Economics, 2018
In this paper we examine mean-field-type games in blockchain-based distributed power networks wit... more In this paper we examine mean-field-type games in blockchain-based distributed power networks with several different entities: investors, consumers, prosumers, producers and miners. Under a simple model of jump-diffusion and regime switching processes, we identify risk-aware mean-field-type optimal strategies for the decision-makers.
Journal of Systems Science and Complexity, 2020
Credit scoring is one of the key problems in financial risk managements. This paper studies the c... more Credit scoring is one of the key problems in financial risk managements. This paper studies the credit scoring problem based on the set-valued identification method, which is used to explain the relation between the individual attribute vectors and classification for the credit worthy and credit worthless lenders. In particular, system parameters are estimated by the set-valued identification algorithm based on a given recognition criteria. In order to illustrate the efficiency of the proposed method, practical experiments are conducted for credit card applicants of Australia and credit card holders from Taiwan, respectively. The empirical results show that the set-valued model has a higher prediction accuracy on both small and large numbers of data set compared with logistic regression model. Furthermore, parameters estimated by the set-valued identification method are more stable, which provide a meaningful and logical explanation for extracting factors that influence the borrowers' credit scorings.
Mathematical Control & Related Fields, 2019
We establish existence of Markov chains of mean-field type with unbounded jump intensities by mea... more We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.
Journal of Network Theory in Finance, 2019
Statistical Methods and Applications in Insurance and Finance, 2016
This is a short introduction to some basic aspects of statistical estimation techniques known as ... more This is a short introduction to some basic aspects of statistical estimation techniques known as graduation technique in life and disability insurance.
Stochastics of Environmental and Financial Economics, 2015
We establish a stochastic maximum principle (SMP) for control problems of partially observed diff... more We establish a stochastic maximum principle (SMP) for control problems of partially observed diffusions of mean-field type with risk-sensitive performance functionals. Keywords Time inconsistent control • Maximum principle • Mean-field SDE • Risk-sensitive control • Partial observation AMS subject classification: 93E20 • 60H30 • 60H10 • 91B28.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Morphisms of backward heat equations preserve, in the appropriate sense, the forward Lagrangian, ... more Morphisms of backward heat equations preserve, in the appropriate sense, the forward Lagrangian, as well as the forward (Newton’s) equations of motion for a general class of diffusions. Time reflection yields results for forward heat equations, in particular for Bernstein-Schrödinger diffusions.
ABSTRACT We suggest an explicit data-driven consistent estimator of the optimal smooth trend in a... more ABSTRACT We suggest an explicit data-driven consistent estimator of the optimal smooth trend in a multivariate Hodrick-Prescott filter, when the associated disturbances (i.e., signal and cycle components) follow a moving average, and a vector autoregressive process, respectively. This is done through deriving consistent estimators of the covariance matrices of the signal and the cycle components. We then fit some macroeconomic data to compare the performances of the associated smooth trend and business cycle with the ones obtained using the estimators of the univariate Hodrick-Prescott filter with auto-correlated disturbances.
In this paper we formulate and solve a mean-field game described by a linear stochastic dynamics ... more In this paper we formulate and solve a mean-field game described by a linear stochastic dynamics and a quadratic or exponential-quadratic cost functional for each generic player. The optimal strategies for the players are given explicitly using a simple and direct method based on square completion and a Girsanov-type change of measure, suggested in Duncan et al. in e.g. [3, 4] for the mean-field free case. This approach does not use the well-known solution methods such as the Stochastic Maximum Principle and the Dynamic Programming Principle with Hamilton-Jacobi-Bellman-Isaacs equation and Fokker-Planck-Kolmogorov equation. In the risk-neutral linear-quadratic mean-field game, we show that there is unique best response strategy to the mean of the state and provide a simple sufficient condition of existence and uniqueness of mean-field equilibrium. This approach gives a basic insight into the solution by providing a simple explanation for the additional term in the robust or risk-sensitive Riccati equation, compared to the risk-neutral Riccati equation. Sufficient conditions for existence and uniqueness of mean-field equilibria are obtained when the horizon length and risk-sensitivity index are small enough. The method is then extended to the linear-quadratic robust mean-field games under small disturbance, formulated as a minimax mean-field game.
EAA Series, 2014
Founded in 1914, the Svenska Aktuarieföreningens Tidskrift (the Journal of the Swedish Society of... more Founded in 1914, the Svenska Aktuarieföreningens Tidskrift (the Journal of the Swedish Society of Actuaries) celebrates its 100 years anniversary in 2014. Today it is, under the name Scandinavian Actuarial Journal (SAJ), a leading international journal of actuarial sciences, and many famous actuaries and mathematicians have been involved in its publications as authors, reviewers or editors.
Scandinavian Actuarial Journal, 1993
A risk process with premiums depending on the current reserve is considered. A large deviation ap... more A risk process with premiums depending on the current reserve is considered. A large deviation approach is used to obtain upper and lower bounds for the corresponding ruin probabilities. They are expressed in terms of the entropy function of the claims distribution
Potential Analysis, 1993
We use ideas from a previous paper by the author to construct a Markov Bernstein process, whose p... more We use ideas from a previous paper by the author to construct a Markov Bernstein process, whose probability density is the product of the solutions of the (imaginary time) Schr6dinger-equation and its adjoint equation, associated to a class of Pauli-type Hamiltonians. A path integral representation of these solutions is obtained as well as the associated regularised Newton equations.
PLoS ONE, 2014
This article examines mean-field games for marriage. The results support the argument that optimi... more This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. 1
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Papers by Boualem Djehiche