I am looking for inspiration and perhaps guidance on the following as I’ve been stuck for a while now:

Context: I am working on a practically oriented project to adjust the Cramér-Lundberg model structures for on-demand insurance (e.g. Trov) and conduct simulations to infer ruin probabilities. However, I am (1) uncertain regarding the optimal model structure and (2) how to go about the simulations.

(1) Model structure: In on-demand insurance, the number of users/insurees is stochastic as opposed to the classical model. I am intending to account for this by using a Markov-modulated risk model where the intensity of the claim arrival process and the “intensity” of the premiums is scaled by the number of active/on users (lambda*on-users). Thus, I want to introduce a Markov-chain to simulate the number of active users.

Ideally, the Markov-chain would reflect the following: fixed or perhaps fluctuating population of potential customers that can transition to active customers. Active customers either stay active or become passive customers which can either stay, become active again or return to the potential state. Is it possible to reflect that situation in a Markov-chain so as to have a stochastically fluctuating number of active customers?

Alternatively, I thought of a simpler birth-death process/chain that models the number of active/on users vs off users.

(2) Simulation: Would be curious to hear your thoughts on the above. Accordingly, if you could point me in the direction of any practical guides tutorials that would be greatly appreciated as well. I came a cross some ruin/actuarial packages in R but am not sure if they can be combined with said Markov-chain. Any ideas on this?


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