This workshop brings together leading experts and young researchers with the goal of promoting information exchange
on recent developments in the broad scope of mathematical finance.

It is organized under the scope of the SANAF project (UTA_CMU/MAT/0006/2009) from the
Fundação para a Ciência e a Tecnologia.

The workshop will be held on Tuesday, December 16, 2014, at the Lisbon School of Economics & Management (ISEG).

Opening session and welcome.

Abstract: We relate solutions of the Navier-Stokes equation (the corresponding Lagrangian and Eulerian flows) to forward-backward stochastic differential systems. In certain cases, by solving these systems, we derive a probabilistic construction of Navier-Stokes solutions.

Free cookies and coffee for everyone :-)

Abstract: This paper extends the static hedge portfolio approach (SHP) of Chung et al. (2013) in two directions. First, the SHP approach is generalized from the constant elasticity of variance (CEV) model of Cox (1975) to the jump to default extended CEV (JDCEV) framework of Carr and Linetsky (2006). For this purpose, the recovery value of the American-style down-and-in put is hedged through the one attached to a European-style plain-vanilla contract whereas for an up-and-in put it is necessary to use the recovery component of the corresponding European-style up-and-in option. Second, and more importantly, the SHP methodology is extended from single to double barrier American-style knock-in options by simply matching the value of the hedging portfolio along both lower and upper barriers. Additionally, and to test the accuracy and efficiency of the novel SHP pricing solutions, the optimal stopping approach of Nunes (2009) is also extended to price American-style double knock-in options under the general JDCEV framework.

Abstract: The principle characteristic of the new technology we model is that customers get access to their own design. This can be achieved e.g. by additive manufacturing (3d printer) or other mass customization technologies. We consider different model variants like a one firm model where the firm needs to determine the optimal time to switch to this new technology, and an incumbent-entrant model where the incumbent produces in an old fashioned way, while the entrant has access to this new technology.

Abstract: We analyse the short-time work (STW) regulations that several OECDcountries introduced during the recent recession. We view these measures as a collection of real options and study the effect of STWon the liquidation decision of the firm. STWdelays a firm?s liquidation, but is not necessarily good for welfare. Moreover, it turns out that firms use STW too long. We show numerically that providers of capital benefit most of STW. Benefits for employees can be negative. A typical Nordic policy performs better than a typical Anglo-Saxon policy for providers of capital, labour, and equity

Abstract: We work two well known models from Risk Theory, the classical Cramer - Lundberg risk model with application to insurance, and the dual risk model with financial application as an investment model. We particularly develop existing duality features between them. These features allow us to retrieve and adapt important results, existing and new, from one to the other. For simplicity the former will be referred as the primal model. The primal has had extensive treatment in the actuarial literature, it assumes that a given surplus process has constant deterministic gains (premiums) and random loses (claims) that come at random times. On the other hand, the latter, denoted as the dual model, works in opposite direction, losses (costs) are constant and deterministic, and the gains (earnings) are random and come at random times. It is also known as the negative risk model. Similar quantities, with similar mathematical properties, work in opposite direction and have different meanings. There is however an important feature that makes the two models distinct, either in their application or in their nature: the loading condition, positive or negative, respectively. The primal model focuses essentially in ruin problems (in many different aspects) whereas the dual model, with a recent development, focuses on dividend payments. In most cases, they have been worked apart, however the obvious connection points allow us to use methods and results from one to the other (mostly, from the first to the second). The right connection is first and clearly addressed by Afonso et al. (2013) for the case when the interarrival times between claims or gains follow an exponential distribution. We can easily understand that the ruin time in the primal has a correspondence to the dividend time in the latter. On the opposite side the time to hit an upper barrier in the primal model has a correspondence to the time to ruin in the dual model. Another interesting feature is the severity of ruin in the former and the size of the dividend payment in the latter.

Abstract: The pricing of financial derivatives with transaction costs is one of the most important extensions of the traditional Black-Scholes model. Stochasic utility maximization models can be used for the pricing of derivatives under these conditions, in this type of models the price is found by computing the certainty equivalent of the portfolio with the option and compare it with the certainty equivalent of the portfolio without the option. One of the most well-known models of this kind was developed by Barles and Soner in 1998, it includes proportional transactions costs and considers an exponential utility function, they use it to price an European Call option. In this paper we present a study on the extension of the model developed by Barles and Soner in terms of a broader type of utility functions (such as HARA-type utility functions) and derivatives payoffs. We make use (as in the original model) of the stochastic dynamic programming principle to find the set of HJB equations whose solution will represent the certainty equivalent of both portfolios. The price of the derivative will be given by the difference of those two functions. We compare the solutions with the original model in particular in terms of the asymptotic analysis of these equations.

Claudia Nunes Philippart (cnunes@math.tecnico.ulisboa.pt)

Raquel Gaspar (raquel.gaspar@iseg.ulisboa.pt)

Manuel Guerra (manuel.guerra@iseg.ulisboa.pt)

Raquel Gaspar (raquel.gaspar@iseg.ulisboa.pt)

Manuel Guerra (manuel.guerra@iseg.ulisboa.pt)

Anfiteatro 1 do Quelhas, 4th floor