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Sirous Fathi Manesh

Sirous Fathi Manesh

Academic rank: Assistant Professor
ORCID:
Education: PhD.
ScopusId: 6473
Faculty: Faculty of Science
Address: Department of Statistics, Faculty of Sciences, University of Kurdistan
Phone:

Research

Title
Some New Ordering Relations for Policy Limits and Deductibles with Homogeneous and Non-Homogeneous
Type
Presentation
Keywords
Arrangement increasing function, exchangeable risks, log-concave functions, majorization, stochastic ordering, risk theory, utility function.
Year
2017
Researchers Sirous Fathi Manesh ، Ebrahim Amini-Seresht

Abstract

Policy limits and deductibles are two common insurance coverage that frequently used by the insurance company. In the policy limit coverage, the company indemnifies the policyholder’s loss up to pre-specified value such as ‎‎‎‎$l‎‎$‎ ‎‎known as the limit amount and if the loss exceeds the remaining loss will be indemnified by the policyholder. In policy deductible coverage, the policyholder is self insured up to pre-specified value such as known as ‎$d‎‎$‎ deductible amount and if the loss exceeds the remaining loss will be covered by the company. \\‎ Let ‎$X_1,...,X_n‎‎$‎ be ‎$n‎‎$‎  risks faced by the policyholder. In policy limit coverage with limit amount ‎$l‎‎$‎ the policyholder should divide ‎$l‎‎$‎  in to ‎$n‎‎$‎  non-negative values ‎$l_1,...,l_n‎‎$‎ such that each ‎$l_i‎‎$‎ is a limit value, taking care of the risk ‎$X_i‎‎$‎ and ‎$\sum_{i=1}{n}l_i=l‎‎$‎. Parallelly, in the policy deductible coverage with deductible amount ‎$d‎‎$‎ the policyholder should divide ‎$d‎‎$‎  in to  non-negative values ‎$d_1,...,d_n‎‎$‎ such that each ‎$d_i‎‎$‎ is a deductible value, taking care of the risk ‎$X_i‎‎$‎ and  ‎$\sum_{i=1}{n}d_i=d‎‎$‎.\\‎ One main concern ,considered in the literature, is how to find an allocation of limits or deductibles that maximizes the expectation of policyholder’s utility or minimizes the remaining risk. Most of the previous works that had been done in this area only focused on the independent or comonotonic risks. In order to extend the previous results, we consider the dependent risks. We assume that the faced risks are exchangeable, arrangement increasing or arrangement decreasing and obtain the best and the worst allocation in each case, for both policy limits and deductibles.