Robust pricing--hedging duality for American options in discrete time financial markets

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a non-dominated family of probability measures. Our first insight is that by considering a (universal) enlargement of the space, we can see American options as European options and recover the pricing-hedging duality, which may fail in the original formulation. This may be seen as a weak formulation of the original problem. Our second insight is that lack of duality is caused by the lack of dynamic consistency and hence a different enlargement with dynamic consistency is sufficient to recover duality: it is enough to consider (fictitious) extensions of the market in which all the assets are traded dynamically. In the second part of the paper we study two important examples of robust framework: the setup of Bouchard and Nutz (2015) and the martingale optimal transport setup of Beiglb\"ock et al. (2013), and show that our general results apply in both cases and allow us to obtain pricing-hedging duality for American options.Comment: 29 page

Ground-state energy of biquadratic spin systems (S=3/2) in the (1/z)1-approximation

Corrections to the molecular-field ground- state energies of the Heisenberg model with isotropic biquadrati c interactions (spin S = 3= 2) are calculated in the ( 1= z ) 1 -approximation using the diagrammatic technique based on the Wick reduction theorem (z is the numb er of spins interacting with any given spin) . The present results for the antiferri- and antiferromagnetic phases complete the previously obtained data for the antiquadrupolar, ferriand ferromagnetic phases. From among the boundaries between different ground states only that b etw een the antiferri- and antiferromagnetic phases is shifted with respect to its molecular-field value

Glycosyltransferase efficiently controls phenylpropanoid pathway

<p>Abstract</p> <p>Background</p> <p>In a previous study, anthocyanin levels in potato plants were increased by manipulating genes connected with the flavonoid biosynthesis pathway. However, starch content and tuber yield were dramatically reduced in the transgenic plants, which over-expressed dihydroflavonol reductase (DFR).</p> <p>Results</p> <p>Transgenic plants over-expressing dihydroflavonol reductase (DFR) were subsequently transformed with the cDNA coding for the glycosyltransferase (UGT) of Solanum sogarandinum in order to obtain plants with a high anthocyanin content without reducing tuber yield and quality. Based on enzyme studies, the recombinant UGT is a 7-O-glycosyltransferase whose natural substrates include both anthocyanidins and flavonols such as kaempferol and quercetin. In the super-transformed plants, tuber production was much higher than in the original transgenic plants bearing only the transgene coding for DFR, and was almost the same as in the control plants. The anthocyanin level was lower than in the initial plants, but still higher than in the control plants. Unexpectedly, the super-transformed plants also produced large amounts of kaempferol, chlorogenic acid, isochlorogenic acid, sinapic acid and proanthocyanins.</p> <p>Conclusion</p> <p>In plants over-expressing both the transgene for DFR and the transgene for UGT, the synthesis of phenolic acids was diverted away from the anthocyanin branch. This represents a novel approach to manipulating phenolic acids synthesis in plants.</p

Chronic lymphocytic inflammation with pontine perivascular enhancement responsive to steroids (CLIPPERS)

The classification and pathological mechanisms of many central nervous system inflammatory diseases remain uncertain. In this article we report eight patients with a clinically and radiologically distinct pontine-predominant encephalomyelitis we have named 'chronic lymphocytic inflammation with pontine perivascular enhancement responsive to steroids' (CLIPPERS). The patients were assessed clinically, radiologically and pathologically at Mayo Clinic, USA and Ghent University Hospital, Belgium from 1999 to 2009. Median follow-up duration from clinical onset was 22 months (range 7-144 months). Patients underwent extensive laboratory (serum and cerebrospinal fluid), radiological and pathological testing (conjunctival, transbronchial and brain biopsies) to search for causes of an inflammatory central nervous system disorder. All eight patients (five female, three male) presented with episodic diplopia or facial paresthesias with subsequent brainstem and occasionally myelopathic symptoms and had a favourable initial response to high dose glucocorticosteroids. All patients had symmetric curvilinear gadolinium enhancement peppering the pons and extending variably into the medulla, brachium pontis, cerebellum, midbrain and occasionally spinal cord. Radiological improvement accompanied clinical response to glucocorticosteroids. Patients routinely worsened following glucocorticosteroid taper and required chronic glucocorticosteroid or other immunosuppressive therapy. Neuropathology of biopsy material from four patients demonstrated white matter perivascular, predominantly T lymphocytic, infiltrate without granulomas, infection, lymphoma or vasculitis. Chronic lymphocytic inflammation with pontine perivascular enhancement responsive to steroids is a definable, chronic inflammatory central nervous system disorder amenable to immunosuppressive treatment. The T cell predominant inflammatory pathology in affected central nervous system lesions and the clinical and radiological response to immunosuppressive therapies is consistent with an immune-mediated process

In Memoriam Marc Yor - Séminaire de Probabilités XLVII

International audienc