On the super replication price of unbounded claims

In an incomplete market the price of a claim f in general cannot be uniquely identified by no arbitrage arguments. However, the ``classical'' super replication price is a sensible indicator of the (maximum selling) value of the claim. When f satisfies certain pointwise conditions (e.g., f is bounded from below), the super replication price is equal to sup_QE_Q[f], where Q varies on the whole set of pricing measures. Unfortunately, this price is often too high: a typical situation is here discussed in the examples. We thus define the less expensive weak super replication price and we relax the requirements on f by asking just for ``enough'' integrability conditions. By building up a proper duality theory, we show its economic meaning and its relation with the investor's preferences. Indeed, it turns out that the weak super replication price of f coincides with sup_{Q\in M_{\Phi}}E_Q[f], where M_{\Phi} is the class of pricing measures with finite generalized entropy (i.e., E[\Phi (\frac{dQ}{dP})]<\infty) and where \Phi is the convex conjugate of the utility function of the investor.Comment: Published at http://dx.doi.org/10.1214/105051604000000459 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A unified framework for utility maximization problems: An Orlicz space approach

We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth, with utility functions that are finite-valued over $(a,\infty)$, $a\in\lbrack-\infty,\infty)$, and satisfy weak regularity assumptions. We adopt a class of trading strategies that allows for stochastic integrals that are not necessarily bounded from below. The embedding of the utility maximization problem in Orlicz spaces permits us to formulate the problem in a unified way for both the cases $a\in\mathbb{R}$ and $a=-\infty$. By duality methods, we prove the existence of solutions to the primal and dual problems and show that a singular component in the pricing functionals may also occur with utility functions finite on the entire real line.Comment: Published in at http://dx.doi.org/10.1214/07-AAP469 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Admissible strategies in semimartingale portfolio selection

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps [HK79]. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over the last twenty years. We propose a novel notion of admissibility that has many pleasant features - admissibility is characterized purely under the objective measure P; each admissible strategy can be approximated by simple strategies using finite number of trading dates; the wealth of any admissible strategy is a supermartingale under all pricing measures; local boundedness of the price process is not required; neither strict monotonicity, strict concavity nor differentiability of the utility function are necessary; the definition encompasses both the classical mean-variance preferences and the monotone expected utility. For utility functions finite on R, our class represents a minimal set containing simple strategies which also contains the optimizer, under conditions that are milder than the celebrated reasonable asymptotic elasticity condition on the utility function.utility maximization; non locally bounded semimartingale; incomplete market; sigma-localization and I-localization; sigma-martingale measure; Orlicz space; convex duality

Absolutely continuous representations of random variables

We study representations of a random variable $\xi$ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the quadratic variation of (local) martingales closed by $\xi$

Wage Rigidity and Retirement in Optimal Portfolio Choice

We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem, which we fully solve obtaining explicitly the optimal controls in feedback form. This is possible as we find an explicit solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is more delicate than in arXiv:2002.00201 to the two-stage structure and to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. Importantly, we discuss not only the optimal allocations for the case of labor income spanned by the traded assets, but also provide novel insights into the case in which wages are also driven by idiosyncratic shocks.Comment: 30 pages, 1 figur

Study of Macrophage Activity in Cats with FIP and Naturally FCoV-Shedding Healthy Cats

Coronavirus frequently infects humans and animals, showing the ability to recombine and cross over to different species. Cats can be considered a model for studying coronavirus infection, in which feline coronavirus (FCoV) represents a major enteric pathogen related to gastroenteric disease. In this animal, the virus can acquire tropism for macrophage cells, leading to a deadly disease called feline infectious peritonitis (FIP). In this study, monocyte-derived macrophages were isolated by CD14-positive selection in venous whole blood from 26 cats with FIP and 32 FCoV-positive healthy cats. Phagocytosis and respiratory burst activities were investigated and compared between the groups. This is the first study comparing macrophage activity in cats affected by FIP and healthy cats positive for FCoV infection. Our results showed that in cats with FIP, the phagocytic and respiratory burst activities were significantly lower. Our results support the possible role of host immunity in Coronaviridae pathogenesis in cats, supporting future research on the immune defense against this systemic disease

Controlled Release of Ibuprofen from Polymeric Nanoparticles

Smart polymeric systems are required that are able to release a therapeutic drug with controlled delivery. Herein we investigated the pH triggered release of ibuprofen from a polymeric nanoparticle system prepared using ring-opening metathesis polymerisation. The co-polymerisation of ibuprofen and poly(ethylene)glycol monomers followed by self-assembly produced a nanoparticle system that was shown to be stable at neutral pH but releases ibuprofen in alkaline condition

Architecture-controlled release of ibuprofen from polymeric nanoparticles

Smart polymeric systems are required that are able to release a therapeutic drug with control over timing and location of delivery. Herein we have investigated the architecture-controlled and pH-triggered release of ibuprofen from a polymeric nanoparticle system prepared using ring-opening metathesis polymerisation. The co-polymerisation of norbornene-derived ibuprofen (NB-Ibu) and poly(ethylene glycol) (NB-PEG) monomers produced polymers with block and random sequence architectures. Self-assembly into nanoparticle systems and release of ibuprofen only under basic conditions was shown to be controlled by polymer sequence