The Department of Statistics at LSE will be hosting our 2nd Risk and Insurance Day organised by LSE Faculty member Dr Daniela Escobar.
We are happy to announce the event will be in-person and we will use a hybrid mode for attendees that cannot join us on campus.
The Risk and Insurance Day at LSE is an event to promote collaboration between researchers at LSE and other universities in this field.
The programme is as follows:
• 10.30am - Welcome & Refreshments
• 10.45am-11.30am – Hirbod Assa (University of Kent) - Risk Management: Lessons from COVID-19
• 11.30am-12.15pm – Erik Baurdoux (LSE) - American multi-asset option pricing under Lévy copulae and the Ballotta-Bonfiglioli model
• 12.15pm-1pm – Andreas Tsanakas (Bayes Business School) - Capital allocation, diversification, and multivariate stress tests
• 1pm-2.45pm – Lunch
• 2.45pm-3.30pm – Silvana Pesenti (University of Toronto) - Sensitivity Measures Based on Scoring Functions
• 3.30pm-4.15pm – Tim Boonen (University of Amsterdam) - (No-)Betting Pareto-Optima under Rank-Dependent Utility
• 4.15pm - Final Remarks
Title and abstracts:
Title: Risk management: lessons from Covid-19
Speaker: Hirbod Assa
Abstract: This seems like another fashionable prevalent popular opportunistic topic leveraging the Covid-19 outbreak just to draw attention. Haven’t we had enough of it? Well, we all are sick of the events in the last three years; I share the same feeling. But, in my opinion, we have not yet touched even the tip of the iceberg. There are many questions that we need to answer in our field of expertise that need years of research. For instance, we haven’t yet managed to answer the following questions: why insurance never was/is a solution, or part of a solution, for such large events? In general, can there be any risk management framework for such large-scale macroeconomic risks? If not why? And if yes, what it must look like?
This is what I want to talk about. In the first half of the talk, I will discuss how risks can be categorized, what the risk management concerns of macro risks are, what the possible arrangements would look like, and what type of errors we need to deal with. Finally, I will discuss that the ex-post policies seem to be the best option and introduce Insurance By Credit (IBC) in that direction. In the second half of the talk, I turn to the mathematics side of the problem and take a look at the highly correlated pool of risk, where the correlation is caused by a common shock. We introduce systematic risk, and systematic event, measure the systematic risk and see how those are related to the principle of pooling as an extension of the principle of insurance. If time allows I will also discuss the risk valuation implications.
Title: American multi-asset option pricing under Lévy copulae and the Ballotta-Bonfiglioli model
Speaker: Erik Baurdoux
Abstract: We consider American options depending on more than one underlying asset in the case that such underlying assets are represented by Lévy processes. We resort to two models to capture the dependence between marginal Lévy processes. Firstly, we model the dependence by copulae and secondly, we consider the Ballotta-Bonfiglioli model, which consists of a reduction scheme in which the marginals are given by the sum of an idiosyncratic part plus a common part.
This talk is based on joint work with Alice Pignatelli di Cerchiara.
Title: Capital allocation, diversification, and multivariate stress tests
Speaker: Andreas Tsanakas
Abstract: Methods for allocating risk capital to portfolio constituents need to address different objectives: a rational treatment of diversification effects, additivity of allocated amounts to the aggregate risk capital, and some level of stability to portfolio changes. Standard Euler-type allocations can fail the latter stability requirements. Specifically, it is possible that reducing risk in one line of business leads to an increase in another line’s capital requirement – a situation that is organisationally undesirable, even if it can be technically justified. Motivated by such considerations, we focus on two particular properties: top-down consistency, that the total capital is determined by the aggregate portfolio risk; and shrinking independence, that the risk capital allocated to a given business line should not be (adversely) affected by a proportional reduction of exposure in another line. We prove an impossibility theorem stating that these two properties jointly lead to the trivial capital allocation based on the mean. Furthermore, we consider allocation methods that are based on multivariate stressing mechanisms, that is, on mappings from random vectors to Radon-Nikodym densities. Driven by dependence considerations, we focus on stressing mechanisms that are invariant to monotonic transformations of risk factors. These ensure that the capital allocated to a line of business depends only on that line’s marginal distribution and the business lines’ copula. Such allocations satisfy shrinking independence, but not top-down consistency, and allow the user to reflect risk diversification/aggregation in different ways. The proposed methods are applied to UK-based non-life portfolio.
This talk is based on joint work with Yuanying Guan, Pietro Millossovich, and Ruodu Wang. It is based on the papers:
Millossovich, P., Tsanakas, A. and Wang, R. (2021). A theory of multivariate stress testing. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3966204
Guan, Y., Tsanakas, A. and Wang, R. (2021). An impossibility theorem on capital allocation. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3964775
Title: Sensitivity Measures Based on Scoring Functions
Speaker: Silvana Pesenti
Abstract: We propose a holistic framework for constructing sensitivity measures for any elicitable functional T of a response variable. The sensitivity measures, termed score-based sensitivities, are constructed via scoring functions that are (strictly) consistent for T. These score-based sensitivities quantify the relative improvement in predictive accuracy when available information, e.g., from explanatory variables, is used ideally. We establish intuitive and desirable properties of these sensitivities and discuss advantageous choices of scoring functions leading to scale-invariant sensitivities.
Since elicitable functionals typically possess rich classes of (strictly) consistent scoring functions, we demonstrate how Murphy diagrams can provide a picture of all score-based sensitivity measures. We discuss the family of score-based sensitivities for the mean functional (of which the Sobol indices are a special case) and risk functionals such as Value-at-Risk, and the pair Value-at-Risk and Expected Shortfall. The sensitivity measures are illustrated using numerous examples, including the Ishigami--Homma test function. In a simulation study, estimation of score-based sensitivities for a non-linear insurance portfolio is performed using neural nets.
This is a joint work with Tobias Fissler, Vienna University of Economics and Business
Title: (No-)Betting Pareto-Optima under Rank-Dependent Utility
Speaker: Tim Boonen
Abstract: In this talk, I discuss a pure-exchange economy with no aggregate uncertainty, and I characterize in closed-form and in full generality Pareto-optimal risk-sharing allocations between two agents who maximize rank-dependent utilities (RDU). I then derive a necessary and sufficient condition for Pareto-optima to be no-betting allocations (i.e., deterministic allocations - or full insurance allocations). This condition depends only on the probability weighting functions of the two agents, and not on their (concave) utility functions. Hence with RDU preferences, it is the difference in probabilistic risk attitudes given common beliefs, rather than heterogeneity or ambiguity in beliefs, that is a driver of a bet. As by-product of our analysis, I answer the question of when sunspots matter in this economy..
Twitter Hashtag for this event: #LSEStatistics