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Uwe Schmock

Publications and source records attributed to Uwe Schmock.

6 recordsLinked to original sources
arXiv2017

Geometry of Distribution-Constrained Optimal Stopping Problems

We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a given probability. The methods work for a large class of cost processes. (At a minimum we need the cost process to be measurable and adapted. Continuity assumptions can be used to guarantee existence of solutions.) We find that for many of the cost processes one can come up with, the solution is given by the first hitting time of a barrier in a suitable phase space. As a by-product we recover classical solutions of the inverse first passage time problem / Shiryaev's problem.

math.PR↗
arXiv2017

Actuarial Applications and Estimation of Extended~CreditRisk$^+$

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk$^+$. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P\&L distributions. Furthermore, the model allows exact (without Monte Carlo simulation error) calculation of risk measures and their sensitivities with respect to model parameters for P\&L distributions such as value-at-risk and expected shortfall. Numerous examples, including an application to partial internal models under Solvency II, using Austrian and Australian data are shown.

q-fin.RM↗
arXiv2016

Crunching Mortality and Life Insurance Portfolios with extended CreditRisk+

Using an extended version of the credit risk model CreditRisk+, we develop a flexible framework with numerous applications amongst which we find stochastic mortality modelling, forecasting of death causes as well as profit and loss modelling of life insurance and annuity portfolios which can be used in (partial) internal models under Solvency II. Yet, there exists a fast and numerically stable algorithm to derive loss distributions exactly, even for large portfolios. We provide various estimation procedures based on publicly available data. Compared to the Lee-Carter model, we have a more flexible framework, get tighter bounds and can directly extract several sources of uncertainty. Straight-forward model validation techniques are available.

q-fin.RM↗
arXiv2015

Forecasting Leading Death Causes in Australia using Extended CreditRisk$+$

Recently we developed a new framework in Hirz et al (2015) to model stochastic mortality using extended CreditRisk$^+$ methodology which is very different from traditional time series methods used for mortality modelling previously. In this framework, deaths are driven by common latent stochastic risk factors which may be interpreted as death causes like neoplasms, circulatory diseases or idiosyncratic components. These common factors introduce dependence between policyholders in annuity portfolios or between death events in population. This framework can be used to construct life tables based on mortality rate forecast. Moreover this framework allows stress testing and, therefore, offers insight into how certain health scenarios influence annuity payments of an insurer. Such scenarios may include improvement in health treatments or better medication. In this paper, using publicly available data for Australia, we estimate the model using Markov chain Monte Carlo method to identify leading death causes across all age groups including long term forecast for 2031 and 2051. On top of general reduced mortality, the proportion of deaths for certain certain causes has changed massively over the period 1987 to 2011. Our model forecasts suggest that if these trends persist, then the future gives a whole new picture of mortality for people aged above 40 years. Neoplasms will become the overall number-one death cause. Moreover, deaths due to mental and behavioural disorders are very likely to surge whilst deaths due to circulatory diseases will tend to decrease. This potential increase in deaths due to mental and behavioural disorders for older ages will have a massive impact on social systems as, typically, such patients need long-term geriatric care.

q-fin.CP↗
arXiv2015

Itô's formula for finite variation Lévy processes: The case of non-smooth functions

Extending Itô's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-Itô, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Itô's formula for diffusion processes where the Meyer-Itô assumptions are weakened even further. We study a version of Itô's formula for multi-dimensional finite variation Lévy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.

q-fin.MF↗