Optimal control of continuous-time Markov chains with noise-free observation

We consider an infinite horizon optimal control problem for a continuous-time Markov chain $X$ in a finite set $I$ with noise-free partial observation. The observation process is defined as $Y_t = h(X_t)$, $t \geq 0$, where $h$ is a given map defined on $I$. The observation is noise-free in the sense that the only source of randomness is the process $X$ itself. The aim is to minimize a discounted cost functional and study the associated value function $V$. After transforming the control problem with partial observation into one with complete observation (the separated problem) using filtering equations, we provide a link between the value function $v$ associated to the latter control problem and the original value function $V$. Then, we present two different characterizations of $v$ (and indirectly of $V$): on one hand as the unique fixed point of a suitably defined contraction mapping and on the other hand as the unique constrained viscosity solution (in the sense of Soner) of a HJB integro-differential equation. Under suitable assumptions, we finally prove the existence of an optimal control

Risk measures and progressive enlargement of filtration: a BSDE approach

We consider dynamic risk measures induced by Backward Stochastic Differential Equations (BSDEs) in enlargement of filtration setting. On a fixed probability space, we are given a standard Brownian motion and a pair of random variables $(\tau, \zeta) \in (0,+\infty) \times E$, with $E \subset \mathbb{R}^m$, that enlarge the reference filtration, i.e., the one generated by the Brownian motion. These random variables can be interpreted financially as a default time and an associated mark. After introducing a BSDE driven by the Brownian motion and the random measure associated to $(\tau, \zeta)$, we define the dynamic risk measure $(\rho_t)_{t \in [0,T]}$, for a fixed time $T > 0$, induced by its solution. We prove that $(\rho_t)_{t \in [0,T]}$ can be decomposed in a pair of risk measures, acting before and after $\tau$ and we characterize its properties giving suitable assumptions on the driver of the BSDE. Furthermore, we prove an inequality satisfied by the penalty term associated to the robust representation of $(\rho_t)_{t \in [0,T]}$ and we discuss the dynamic entropic risk measure case, providing examples where it is possible to write explicitly its decomposition and simulate it numerically.Comment: 30 pages, 2 figure

Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics

The objective of this paper is to study the filtering problem for a system of partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump process representing the signal and $Y$ is a general jump-diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filtering process via the innovations approach

Infinite Dimensional Control Problems with Positivity State Constraints: a Banach Lattice Approach

This paper is devoted to studying a family of deterministic optimal control problems in an infinite dimension. The difficult feature of such problems is the presence of positivity state constraints, which arise very often in economic applications (our main motivation). To deal with such constraints we set up the problem in a Banach space with a Riesz space structure (i.e., a Banach lattice) and not necessarily reflexive, like $\mathcal{C}^0$. In this setting, which seems to be new in this context, we are able, using a type of infinite-dimensional Perron-Frobenius Theorem, to find explicit solutions of the HJB equation associated to a suitable auxiliary problem and to use such results to get information about the optimal paths of the starting problem. This was not possible to perform in the previously used infinite-dimensional setting where the state space was an $\mathrm{L}^2$ space

Notulae to the Italian alien vascular flora 6

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions of taxa in the genera Acalypha, Acer, Canna, Cardamine, Cedrus, Chlorophytum, Citrus, Cyperus, Epilobium, Eucalyptus, Euphorbia, Gamochaeta, Hesperocyparis, Heteranthera, Lemna, Ligustrum, Lycium, Nassella, Nothoscordum, Oenothera, Osteospermum, Paspalum, Pontederia, Romulea, Rudbeckia, Salvia, Sesbania, Setaria, Sicyos, Styphnolobium, Symphyotrichum, and Tradescantia. Nomenclature and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Notulae to the Italian native vascular flora: 8

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations, exclusions, and status changes to the Italian administrative regions for taxa in the genera Ajuga, Chamaemelum, Clematis, Convolvulus, Cytisus, Deschampsia, Eleocharis, Epipactis, Euphorbia, Groenlandia, Hedera, Hieracium, Hydrocharis, Jacobaea, Juncus, Klasea, Lagurus, Leersia, Linum, Nerium, Onopordum, Persicaria, Phlomis, Polypogon, Potamogeton, Securigera, Sedum, Soleirolia, Stachys, Umbilicus, Valerianella, and Vinca. Nomenclatural and distribution updates, published elsewhere, and corrigenda are provided as Suppl. material 1

Notulae to the Italian alien vascular flora: 12

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates published elsewhere are provided as Suppl. material 1

Notulae to the Italian native vascular flora: 6

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations and status changes to the Italian administrative regions for taxa in the genera Alchemilla, Arundo, Bupleurum, Clematis, Clinopodium, Cota, Crassula, Cytisus, Euphorbia, Hieracium, Isoëtes, Lamium, Leontodon, Linaria, Lychnis, Middendorfia, Ophrys, Philadelphus, Pinus, Sagina, Sedum, Taeniatherum, Tofieldia, Triticum, Veronica, and Vicia. Nomenclature and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Notulae to the Italian native vascular flora: 6

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations and status changes to the Italian administrative regions for taxa in the genera Alchemilla, Arundo, Bupleurum, Clematis, Clinopodium, Cota, Crassula, Cytisus, Euphorbia, Hieracium, Isoëtes, Lamium, Leontodon, Linaria, Lychnis, Middendorfia, Ophrys, Philadelphus, Pinus, Sagina, Sedum, Taeniatherum, Tofieldia, Triticum, Veronica, and Vicia. Nomenclature and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Il ruolo dell’informazione nella misurazione dei rischi finanziari: un approccio quantitativo

1noopenopenAlessandro CalviaCalvia, Alessandr