In this review paper we try to describe some recent results on modeling and analysis of
economic risks by using the techniques of fractional calculus. The use of fractional order …

This paper defines a new class of fractional differential operators alongside a family of
random variables whose density functions solve fractional differential equations equipped …

In this study, we consider a linear Volterra integral equation of the second type whose
unique unknown solution is known to be Lipschitz-continuous. Using this property, we derive …

In this paper, we study the problem of solving Seal's type partial integro-differential
equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep …

This paper considers a Cramér–Lundberg risk setting, where the components of the
underlying model change over time. We allow the more general setting of the cumulative …

In this paper, we introduce a compound version of the mixed fractional Poisson process
(MFPP). We obtain its mean, variance and the system of fractional differential equations that …

Sensitivity analysis investigates how the change in the output of a computational model can
be attributed to changes of its input parameters. Identifying the input parameters that …

In the classical risk process, ruin is the situation when the surplus falls below zero. Ruin
probability is a tool used to predict bankruptcy in the insurance company. The ruin …

A new procedure to find the ultimate ruin probability in the Cramér-Lundberg risk model is
presented for claims with a mixture of m Erlang distributions. The method requires to solve …

In risk theory, the resolutions of many interesting problems are reduced to solving some
integro-differential equations (IDE), see [4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 21, 22, 23, 24, 25 …