Optimal switching problems with an infinite set of modes: An approach by randomization and constrained backward SDEs

We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes, i.e. the possible values of the piecewise-constant control process). We allow all the given coefficients in the model to be path-dependent, that is, their value at any time depends on the past trajectory of the controlled system. The main aim is to introduce a suitable (scalar) backward stochastic differential equation (BSDE), with a constraint on the martingale part, that allows to give a probabilistic representation of the value function of the given problem. This is achieved by randomization of control, i.e. by introducing an auxiliary optimization problem which has the same value as the starting optimal switching problem and for which the desired BSDE representation is obtained. In comparison with the existing literature we do not rely on a system of reflected BSDE nor can we use the associated Hamilton\u2013Jacobi\u2013Bellman equation in our non-Markovian framework

Utility maximization with random horizon: a BSDE approach

International audienceIn this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations

On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori $L^{\infty}$-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.Comment: 28 pages. Added DOI https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final publication, corrected typo (missing gamma) in example 4.1

Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Variation in susceptibility of African Plasmodium falciparum malaria parasites to TEP1 mediated killing in Anopheles gambiae mosquitoes

Anopheles gambiae s.s. mosquitoes are efficient vectors for Plasmodium falciparum, although variation exists in their susceptibility to infection. This variation depends partly on the thioester-containing protein 1 (TEP1) and TEP depletion results in significantly elevated numbers of oocysts in susceptible and resistant mosquitoes. Polymorphism in the Plasmodium gene coding for the surface protein Pfs47 modulates resistance of some parasite laboratory strains to TEP1-mediated killing. Here, we examined resistance of P. falciparum isolates of African origin (NF54, NF165 and NF166) to TEP1-mediated killing in a susceptible Ngousso and a refractory L3-5 strain of A. gambiae. All parasite clones successfully developed in susceptible mosquitoes with limited evidence for an impact of TEP1 on transmission efficiency. In contrast, NF166 and NF165 oocyst densities were strongly reduced in refractory mosquitoes and TEP1 silencing significantly increased oocyst densities. Our results reveal differences between African P. falciparum strains in their capacity to evade TEP1-mediated killing in resistant mosquitoes. There was no significant correlation between Pfs47 genotype and resistance of a given P. falciparum isolate for TEP1 killing. These data suggest that polymorphisms in this locus are not the sole mediators of immune evasion of African malaria parasites

Unravelling the immune signature of Plasmodium falciparum transmission-reducing immunity

Infection with Plasmodium can elicit antibodies that inhibit parasite survival in the mosquito, when they are ingested in an infectious blood meal. Here, we determine the transmission-reducing activity (TRA) of naturally acquired antibodies from 648 malaria-exposed individuals using lab-based mosquito-feeding assays. Transmission inhibition is significantly associated with antibody responses to Pfs48/45, Pfs230, and to 43 novel gametocyte proteins assessed by protein microarray. In field-based mosquito-feeding assays the likelihood and rate of mosquito infection are significantly lower for individuals reactive to Pfs48/45, Pfs230 or to combinations of the novel TRA-associated proteins. We also show that naturally acquired purified antibodies against key transmission-blocking epitopes of Pfs48/45 and Pfs230 are mechanistically involved in TRA, whereas sera depleted of these antibodies retain high-level, complement-independent TRA. Our analysis demonstrates that host antibody responses to gametocyte proteins are associated with reduced malaria transmission efficiency from humans to mosquitoes

Low linkage disequilibrium in wild Anopheles gambiae s.l. populations

<p>Abstract</p> <p>Background</p> <p>In the malaria vector <it>Anopheles gambiae</it>, understanding diversity in natural populations and genetic components of important phenotypes such as resistance to malaria infection is crucial for developing new malaria transmission blocking strategies. The design and interpretation of many studies here depends critically on Linkage disequilibrium (LD). For example in association studies, LD determines the density of Single Nucleotide Polymorphisms (SNPs) to be genotyped to represent the majority of the genomic information. Here, we aim to determine LD in wild <it>An. gambiae s.l</it>. populations in 4 genes potentially involved in mosquito immune responses against pathogens (<it>Gambicin</it>, <it>NOS</it>, <it>REL2 </it>and <it>FBN9</it>) using previously published and newly generated sequences.</p> <p>Results</p> <p>The level of LD between SNP pairs in cloned sequences of each gene was determined for 7 species (or incipient species) of the <it>An. gambiae </it>complex. In all tested genes and species, LD between SNPs was low: even at short distances (< 200 bp), most SNP pairs gave an r²< 0.3. Mean r²ranged from 0.073 to 0.766. In most genes and species LD decayed very rapidly with increasing inter-marker distance.</p> <p>Conclusions</p> <p>These results are of great interest for the development of large scale polymorphism studies, as LD generally falls below any useful limit. It indicates that very fine scale SNP detection will be required to give an overall view of genome-wide polymorphism. Perhaps a more feasible approach to genome wide association studies is to use targeted approaches using candidate gene selection to detect association to phenotypes of interest.</p

Positional cloning of rp2 QTL associates the P450 genes CYP6Z1, CYP6Z3 and CYP6M7 with pyrethroid resistance in the malaria vector Anopheles funestus

Pyrethroid resistance in Anopheles funestus is threatening malaria control in Africa. Elucidation of underlying resistance mechanisms is crucial to improve the success of future control programs. A positional cloning approach was used to identify genes conferring resistance in the uncharacterised rp2 quantitative trait locus (QTL) previously detected in this vector using F6 advanced intercross lines (AIL). A 113 kb BAC clone spanning rp2 was identified and sequenced revealing a cluster of 15 P450 genes and one salivary protein gene (SG7-2). Contrary to A. gambiae, AfCYP6M1 is triplicated in A. funestus, while AgCYP6Z2 orthologue is absent. Five hundred and sixty-five new single nucleotide polymorphisms (SNPs)were identified for genetic mapping from rp2 P450s and other genes revealing high genetic polymorphisms with one SNP every 36 bp. A significant genotype/phenotype association was detected for rp2 P450s but not for a cluster of cuticular protein genes previously associated with resistance in A. gambiae. QTL mapping using F6 AIL confirms the rp2 QTL with an increase logarithm of odds score of 5. Multiplex gene expression profiling of 15 P450s and other genes around rp2 followed by individual validation using qRT–PCR indicated a significant overexpression in the resistant FUMOZ-R strain of the P450s AfCYP6Z1, AfCYP6Z3, AfCYP6M7 and the glutathione-s-transferase GSTe2 with respective fold change of 11.2,6.3, 5.5 and 2.8. Polymorphisms analysis of AfCYP6Z1 and AfCYP6Z3 identified amino acid changes potentially associated with resistance further indicating that these genes are controlling the pyrethroid resistance explained by the rp2 QTL. The characterisation of this rp2 QTL significantly improves our understanding of resistance mechanisms in A. funestus