Hampus Engsner


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Arbetar vid Matematiska institutionen
Telefon 08-16 45 07
Besöksadress Kräftriket hus 6
Rum 319
Postadress Matematiska institutionen 106 91 Stockholm

Om mig

I am a PhD student in insurance mathematics


My main research interest is probability theory and stochastic processes, as it pertains to insurance related problems.

Publications and preprints:

  • 2020. Engsner, H.,  Lindskog, F.:
    Continuous-time limits of multi-period cost-of-capital margins
    Statistics & Risk Modeling. Ahead of print. Published online 2020-04-17
    Open access:
  • 2020. Engsner, H., Lindensjö, K., Lindskog, F.:
    The value of a liability cash flow in discrete time subject to capital requirements Finance and Stochastics, 24 (2020) pp. 125-167.
    Open access:
  • 2017. Engsner, H., Lindholm, M., Lindskog, F.:
    Insurance valuation: a computable multi-period cost-of-capital approach
    Insurance Mathematics and Economics: 72 (2017) pp. 250-264.


I urval från Stockholms universitets publikationsdatabas
  • 2017. Hampus Engsner, Mathias Lindholm, Filip Lindskog. Insurance, Mathematics & Economics 72, 250-264

    We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.

  • 2018. Hampus Engsner (et al.).

    In the papers presented here, approaches to multi-period valuation of a liability cashflow in runoff, subject to repeated capital requirements, are developed and analyzed. The valuation approaches are inspired by current risk-based regulatory frameworks for the insurance industry, and consistent with the fundamental principles underlying them. The capital requirements are partly financed by capital providers with limited liability, meaning that the capital providers cannot lose more than the provided capital. Limited liability is an essential ingredient in the considered multi-period valuation framework.

    In the first paper, multi-period cost-of-capital valuation is considered. The liability value is defined in terms of the capital provider's criterion for accepting to provide capital which gives rise to a backward recursion from which the liability value can be computed. Explicit solutions to the recursion are obtained when the cashflows can be expressed in terms of multivariate Gaussian distributions.

    The second paper recognizes that due to limited liability (an option to default) the cashflow to the capital provider can be seen as that of a financial derivative instrument with optionality. Arbitrage-free valuation of this cashflow, similar to the valuation of so-called American type contingent claims, forms the basis of the multi-period approach to liability cashflow valuation considered here. The issue of selection of a replicating portfolio for offsetting the hedgeable part of the liability cashflow is investigated.

    The first two papers consider cashflows and valuations at a fixed set of times to be interpreted as the years from current time until the runoff of the liability is complete. In the third paper, the valuation and cashflow times are allowed to be arbitrary in the form of an arbitrary partition of the entire runoff period. The focus here is to properly define and analyze the effects of letting the mesh of the partition tend to zero, exploring the continuous-time value processes that appear.

  • 2018. Hampus Engsner, Filip Lindskog.

    We consider multi-period cost-of-capital valuation of a liability cashflow subject to repeated capital requirements that are partly financed by capital injections from capital providers with limited liability. Limited liability means that, in any given period, the capital provider is not liable for further payment in the event that the capital provided at the beginning of the period turns out to be insufficient to cover both the current-period payments and the updated value of the remaining cash flow. The liability cash flow is modeled as a continuous-time stochastic process on [0, T]. The multi-period structure is given by apartition of [0, T] into subintervals, and on the corresponding finite set of times a discrete-time value process is defined. Our main objectiveis the analysis of existence and properties of continuous-time limits of discrete-time value processes corresponding to a sequence of partitions whose meshes tend to zero. Moreover, we provide explicit and interpretable valuation formulas for a wide class of cash flow models.

  • Hampus Engsner, Kristoffer Lindensjö, Filip Lindskog.

    The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the approach presented is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner's perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.

Visa alla publikationer av Hampus Engsner vid Stockholms universitet

Senast uppdaterad: 10 juni 2020

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