14:15
Explicit Construction of a Dynamic Bessel Bridge of Dimension 3
Abstract
Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V (t) satisfies $V (t) > t$ for all $t>=0$, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V (s), where $s:= inf {t > 0 : Z_t = 0}$. We also provide the semimartingale decomposition of $X >$ under
the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time $V (s)$.
We call this a dynamic Bessel bridge since V(s) is not known in advance. Our study is motivated by insider trading models with default risk.(this is a joint work with Luciano Campi and Umut Cetin)
Analytical Results on the PAUSE Auction Procedure
Abstract
In this talk, we focus on the analytical properties of a decentralized auction, namely the PAUSE Auction Procedure. We prove that the revenue of the auctioneer from PAUSE is greater than or equal to the profit from the well-known VCG auction when there are only two bidders and provide lower bounds on the profit for arbitrary number of bidders. Based on these bounds and observations from auctions with few items, we propose a modification of the procedure that increases the profit. We believe that this study, which is still in progress, will be a milestone in designing better decentralized auctions since it is the first analytical study on such auctions with promising results.
14:15
Inf-convolution of convex risk emasures and optimal risk transfer
Abstract
We develop a methodology to optimally design a financial issue to hedge
non-tradable risk on financial markets.The modeling involves a minimization
of the risk borne by issuer given the constraint imposed by a buyer who
enters the transaction if and only if her risk level remains below a given
threshold. Both agents have also the opportunity to invest all their residual
wealth on financial markets but they do not have the same access to financial
investments. The problem may be reduced to a unique inf-convolution problem
involving some transformation of the initial risk measures.