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28/05/2020, 11:00 — 12:00 — Online

Cláudia Nunes, *CEMAT-IST*

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Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations

In this talk we address, in the context of real options, an investment problem with two sources of uncertainty: the price (reflected in the revenue of the firm) and the level of technology. The level of technology impacts in the investment cost, that decreases when there is a technology innovation. The price follows a geometric Brownian motion, whereas the technology innovations are driven by a Poisson process. As a consequence, the investment region may be attained in a continuous way (due to an increase of the price) or in a discontinuous way (due to a sudden decrease of the investment cost).

For this optimal stopping problem no analytical solution is known, and therefore we propose a quasi-analytical method to find an approximated solution that preserves the qualitative features of the exact solution. This method is based on a truncation procedure and we prove that the truncated solution converges to the solution of the original problem.

We provide results for the comparative statics for the investment thresholds. These results show interesting behaviors, particularly, the investment may be postponed or anticipated with the intensity of the technology innovations and with their impact on the investment cost.

(joint work with Carlos Oliveira and Rita Pimentel)

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18/06/2020, 11:00 — 12:00 Europe/Lisbon —
Online

Igor Kravchenko, *CEMAT-IST*

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Investment problem with switching modes

In this talk we will look at the optimal control problem of a firm that may operate in two different modes, one being more risky than the other, in the sense that in case the demand decreases, the return of the risky mode is lower than with the more conservative mode. On the other side, in case the demand increases, the opposite holds. The switches between these two alternative modes have associated costs. In both modes, there is the option to exit the market.

We will focus on two different parameter scenarios, that describe particular (and somehow extreme) economic situations. In the first scenario, we assume that the market is expected to increase in such a way that once the firm is producing in the more risky mode, it is never optimal to switch to the more conservative one. In the second scenario, there is a hysteresis region, where the firm is waiting in the more risky mode, in production, until some drop or increase in the demand leads to an exit or changing to the more conservative mode. This hysteresis region cannot be attained under continuous production.

We then address the problem of the optimal time to invest under each situation. Depending on the relation between the switching costs (equal or different from one mode to another), it may happen that the firm invests in the hysteresis region.

Joint work with Cláudia Nunes and Carlos Oliveira

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02/07/2020, 11:00 — 12:00 Europe/Lisbon —
Online

Joaquim Ferreira, *FMUL and IMM*

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COVID, uncertainty and clinical trials

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16/07/2020, 11:00 — 12:00 Europe/Lisbon —
Online

Miguel de Carvalho, *University of Edinburgh*

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Elements of Bayesian geometry

In this talk, I will discuss a geometric interpretation to Bayesian inference that will yield a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of the proposed geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.

Joint work with G. L. Page and with B. J. Barney