Lectures on Insurance Models

verfasst von: S. Ramasubramanian

Verlag: Hindustan Book Agency

Buchreihe : Texts and Readings in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Catastrophes, natural as well as man-made, reinforce the fact that almost everyone would like to be assured of some (non-supernatural) agency to bank upon in times of grave need. If the affected parties are too poor, then it is the responsibility of governments and the “haves” to come to the rescue. It is not uncommon that places of worship, palatial buildings and schools serve as refuges for the affected. However, there are also significant sections of the population who are willing to pay regular premium to suitable agencies during normal times to have insurance cover to tide over crises.

S. Ramasubramanian

Chapter 2. Poisson model

Abstract

We first consider the claim number process {N(t) : t ≥ 0}. We assume that there is a basic probability space(Ω, ℱ, P) on which N (t, •) is a random variable for each t ≥ 0. We list below some of the obvious/desired properties of N (raither postulates for N), which may be taken into account in formulating a model for the claim number process.

S. Ramasubramanian

Chapter 3. Renewal model

Abstract

Renewal process is a generalization of the homogeneous Poisson process obtained by dropping the assumption of exponential interarrival times. The corresponding counting process will serve as a model for claim number process. Our approach in this chapter relies heavily on [Fe], [RSST]. All the random variables are defined on a probability space (Ω, ℱ, P).

S. Ramasubramanian

Chapter 4. Claim size distributions

Abstract

In principle, any distribution supported on [0, ∞) can be used to model claim size. However, in actuarial practice a clear distinction is made between “well behaved” distributions and “dangerous” distributions. As we shall see later there are very good reasons for this distinction.

S. Ramasubramanian

Chapter 5. Ruin Problems

Abstract

Ruin probability is the probability of the insurance company getting ruined in finite time. It is considered to be a reasonably objective indicator of the health of the company. So problems centering around ruin probability have a prominent place in mathematical analysis of insurance models. We shall first consider some general results in the Sparre Andersen model; later we shall specialise to the case of the Cramér-Lundberg model.

S. Ramasubramanian

Chapter 6. Lundberg risk process with investment

Abstract

Around the same time Lundberg formulated his risk model, French mathematician Louis Bachelier worked out a quantitative theory of Brownian motion from a study of stock price fluctuations. (It is interesting to note that Bachelier’s pioneering work predated the famous work of Einstein on Brownian motion by five years!) Though risk models perturbed by Brownian motion/Levy process and diffusion approximation of risk processes have been studied since 1970’s, (see Chapter 13 of [RSST]), interaction between these two important stochastic models has been sporadic till recently.

S. Ramasubramanian

Backmatter

Titel: Lectures on Insurance Models
verfasst von: S. Ramasubramanian
Verlag: Hindustan Book Agency
Electronic ISBN: 978-93-86279-44-6
Print ISBN: 978-81-85931-93-7
DOI: https://doi.org/10.1007/978-93-86279-44-6