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Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension
(2011)arXivThe purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch ...Working Paper -
The Price of Matching Selfish Vertices
(2011)arXivWe analyze the setting of minimum-cost perfect matchings with selfish vertices through the price of anarchy (PoA) and price of stability (PoS) lens. The underlying solution concept used for this analysis is the Gale-Shapley stable matching notion, where the preferences are determined so that each player (vertex) wishes to minimize the cost of her own matching edge.Working Paper -
A new family of representations of virtually free groups
(2011)arXivWe construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the regular representation, thus implying that all the representations in this family can be realized on the boundary of L. As a corollary, we obtain an analogue of Herz majorization principle.Working Paper -
Affine processes on symmetric cones
(2011)arXivWe consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in an irreducible symmetric cone in terms of certain L\'evy-Khintchine triplets. This is the complete classification of affine processes on these conic state spaces, thus extending the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (1991).Working Paper -
Higher Teichmüller Spaces
(2011)arXivThe first part of this paper surveys several characterizations of Teichm\"uller space as a subset of the space of representation of the fundamental group of a surface into PSL(2,R). Special emphasis is put on (bounded) cohomological invariants which generalize when PSL(2,R) is replaced by a Lie group of Hermitian type. The second part discusses underlying structures of the two families of higher Teichm\"uller spaces, namely the space of ...Working Paper -
Weakly maximal representations of surface groups
(2011)arXivWe introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maximal representations. We prove that weakly maximal representations are discrete and injective and describe the structure of the Zariski closure of the image. An interesting feature of these ...Working Paper -
Local Volatility of Volatility for the VIX market
(2011)NCCR Finrisk Working PaperFollowing a trend of sustained and accelerated growth, the VIX futures and options market has become a closely followed, active and liquid market. The standard stochastic volatility models --which focus on the modeling of instantaneous variance -- are unable to fit the entire term structure of VIX futures as well as the entire VIX options surface. In contrast, we propose to model directly the VIX index, in a mean-reverting local ...Working Paper -
Mean-Variance Hedging via Stochastic Control and BSDEs for General Semimartingales
(2011)NCCR Finrisk Working PaperWe solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterise its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional ...Working Paper -
General Equilibrium with Multi-Member Households and Production
(2011)CESifo Working PapersWe consider firms and multi-member households operating in a competitive market environment. Households are endowed with resources (commodity bundles) and shares of firm ownership. Household members are characterized by individual preferences, possibly with intra-household consumption externalities. Household decisions adhere to the collective rationality model. Existence of general equilibrium and validity of the first welfare theorem ...Working Paper -