Data and uncertainty in extreme risks - a nonlinear expectations approach

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [5] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting

Representing filtration consistent nonlinear expectations as gg-expectations in general probability spaces

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob-Meyer decomposition of Peng to a general context

Automated soil hardness testing machine

This paper describes the design and performance of a mechatronic system for controlling a standard drop-hammer mechanism that is commonly used in performing outdoor soil or ground hardness tests. A low-cost microcontroller is used to control a hydraulic actuator to repeatedly lift and drop a standard free-falling weight that strikes a pipe (sampler) which is pushed deeper into the ground with each impact. The depth of the sampler pipe and position of the hydraulic cylinder are constantly monitored and the number of drops, soil penetration data and other variables are recorded in a database for future analysis. This device, known as the “EVH Trip Hammer”, allows the full automation and faster completion of what is typically a very labour-intensive and slow testing process that can involve human error and the risk of human injuries

A Marketing Booklet for the Square Apartel & Arcade: a Way to Attract More Customers to the Hotel

The Square Apartel & Arcade is a new exclusive apartelle (a mixture of apartment and hotel) with a “one stop living” concept. It is located at Siwalankerto Street 146 – 148, Surabaya, East-Java, Indonesia. It is divided into two different types of business; an apartment and a hotel. In reality, many people think that The Square Apartel & Arcade only provides apartments, not lodgings. Therefore, it has become a problem for The Square. To solve this problem, The Square needs a media which can help its owner to show the real business of The Square, i.e. apartment and hotel. As a result, the writer decided to make a marketing booklet which contains eight parts: table of contents, company overview (“About The Square Apartel & Arcade”), product description (“Room Types”), the price of the product (“Room Rates”), additional services, building facilities, shopping arcade, and contact information (“Contact Us”). By having all the information above, prospective customers would have more precise information about the business of The Square. Hopefully, this marketing booklet will enable The Square to attract and get more customer

Ergodic BSDEs with jumps and time dependence

In this paper we look at ergodic BSDEs in the case where the forward dynamics are given by the solution to a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck SDE with L\'evy noise, taking values in a separable Hilbert space. We establish the existence of a unique bounded solution to an infinite horizon discounted BSDE. We then use the vanishing discount approach, together with coupling techniques, to obtain a Markovian solution to the EBSDE. We also prove uniqueness under certain growth conditions. Applications are then given, in particular to risk-averse ergodic optimal control and power plant evaluation under uncertainty

Nash equilibria for non zero-sum ergodic stochastic differential games

In this paper we consider non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a Nash equilibrium under the generalised Isaac's conditions. We also study the case of interacting players of different type