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Giorgio Ferrari

Publications and source records attributed to Giorgio Ferrari.

At least 91 records · Page 5Linked to original sources

All-optical mode unscrambling on a silicon photonic chip

Propagation of light beams through scattering or multimode systems may lead to randomization of the spatial coherence of the light. Although information is not lost, its recovery requires a coherent interferometric reconstruction of the original signals, which have been scrambled into the modes of the scattering system. Here, we show that we can automatically unscramble four optical beams that have been arbitrarily mixed in a multimode waveguide, undoing the scattering and mixing between the spatial modes through a mesh of silicon photonics Mach-Zehnder interferometers. Using embedded transparent detectors and a progressive tuning algorithm, the mesh self-configures automatically and reset itself after significantly perturbing the mixing, without turning off the beams. We demonstrate the recovery of four separate 10 Gbits/s information channels, with residual cross-talk between beams of -20dB. This principle of self-configuring and self-resetting in optical systems should be applicable in a wide range of optical applications.

physics.ins-det↗

Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a Skorohod reflection problem at a suitable boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems and it is characterized in terms of the family of unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm type.

math.PR↗

Optimal Entry to an Irreversible Investment Plan with Non Convex Costs

A problem of optimally purchasing electricity at a real-valued spot price (that is, with potentially negative cost) has been recently addressed in De Angelis, Ferrari and Moriarty (2015) [SIAM J. Control Optim. 53(3)]. This problem can be considered one of irreversible investment with a cost functional which is non convex with respect to the control variable. In this paper we study the optimal entry into this investment plan. The optimal entry policy can have an irregular boundary arising from this non convexity, with a kinked shape.

math.OC↗

A solvable two-dimensional singular stochastic control problem with non convex costs

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.

math.OC↗

Continuous-Time Public Good Contribution under Uncertainty: A Stochastic Control Approach

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner's optimal policy, we characterize it by necessary and sufficient stochastic Kuhn-Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.

math.OC↗

Optimal Dynamic Procurement Policies for a Storable Commodity with Lévy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential Lévy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.

math.OC↗

On an integral equation for the free-boundary of stochastic, irreversible investment problems

In this paper, we derive a new handy integral equation for the free-boundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion $X$. The new integral equation allows to explicitly find the free-boundary $b(\cdot)$ in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and $X$ is a three-dimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that $b(X(t))=l^*(t)$, with $l^*$ the unique optional solution of a representation problem in the spirit of Bank-El Karoui [Ann. Probab. 32 (2004) 1030-1067]; then, thanks to such an identification and the fact that $l^*$ uniquely solves a backward stochastic equation, we find the integral problem for the free-boundary.

q-fin.PM↗

ContactLess Integrated Photonic Probe for light monitoring in InP-based devices

The increasing complexity of photonic integrated circuits requires the possibility to monitor the state of the circuit in order to stabilize the working point against environmental fluctuations or to perform reliable reconfiguration procedures. Although InP technologies can naturally integrate high-quality photodiodes, their use as tap monitors necessarily affects the circuit response and is restricted to few units per chip. They are hence unsuited for very large circuits, where transparent power monitors become key components. In this paper we present the implementation of a ContactLess Integrated Photonic Probe (CLIPP) realizing a non invasive integrated light monitor on InP-based devices. We describe an innovative vertical scheme of the CLIPP monitor which exploits the back side of the chip as a common electrode, thus enabling a reduction of the device footprint and a simplification of the electrical connectivity. We characterize the response of the CLIPP and demonstrate its functionality as power monitor. Lastly, we provide a direct demonstration that CLIPP monitor allows to access more accurate information on the working point of photonic integrated circuits compared to conventional external or integrated photodetectors.

physics.optics↗

A Stochastic Partially Reversible Investment Problem on a Finite Time-Horizon: Free-Boundary Analysis

We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investment-disinvestment problem a zero-sum optimal stopping game and characterize its value function through a free-boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries.

math.OC↗

A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries

Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a non convex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyse the geometry of the action and inaction regions by characterising their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping.

math.OC↗

Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary

We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting, we show that the optimal boundary is intimately linked to the unique optional solution of an appropriate Bank-El Karoui representation problem. Such a relation and the Wiener Hopf factorization allow us to derive an integral equation for the optimal investment boundary. In case the underlying Lévy process hits any real point with positive probability we show that the integral equation for the investment boundary is uniquely satisfied by the unique solution of another equation which is easier to handle. As a remarkable by-product we prove the continuity of the optimal investment boundary. The paper is concluded with explicit results for profit functions of (i) Cobb-Douglas type and (ii) CES type. In the first case the function is separable and in the second case non-separable.

q-fin.PM↗

Non-invasive monitoring and control in silicon photonics by CMOS integrated electronics

As photonics breaks away from today's device level toward large scale of integration and complex systems-on-a-chip, concepts like monitoring, control and stabilization of photonic integrated circuits emerge as new paradigms. Here, we show non-invasive monitoring and feedback control of high quality factor silicon photonics resonators assisted by a transparent light detector directly integrated inside the cavity. Control operations are entirely managed by a CMOS microelectronic circuit, hosting many parallel electronic read-out channels, that is bridged to the silicon photonics chip. Advanced functionalities, such as wavelength tuning, locking, labeling and swapping are demonstrated. The non-invasive nature of the transparent monitor and the scalability of the CMOS read-out system offer a viable solution for the control of arbitrarily reconfigurable photonic integrated circuits aggregating many components on a single chip.

physics.optics↗

Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem

We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal investment process. That is a singular stochastic control problem. We derive some first order conditions for optimality and we characterize the optimal solution in terms of the base capacity process, i.e. the unique solution of a representation problem in the spirit of Bank and El Karoui (2004). We show that the base capacity is deterministic and it is identified with the free boundary of the associated optimal stopping problem, when the coefficients of the controlled diffusion are deterministic functions of time. This is a novelty in the literature on finite horizon singular stochastic control problems. As a subproduct this result allows us to obtain an integral equation for the free boundary, which we explicitly solve in the infinite horizon case for a Cobb-Douglas production function and constant coefficients in the controlled capacity process.

math.OC↗

Non-invasive light observer

Photonic technologies lack non-invasive monitoring tools to inspect the light inside optical waveguides. This is one of the main barriers to large scale of integration, even though photonic platforms are potentially ready to host several thousands of elements on a single chip. Here, we demonstrate non-invasive light observation in silicon photonics devices by exploiting photon interaction with intra-gap energy states localized at the waveguide surface. Light intensity is measured through a ContactLess Integrated Photonic Probe (CLIPP) that introduces no measurable extra-photon absorption and a phase perturbation as low as 0.2 mrad, comparable to thermal fluctuations of less than 3 mK. Multipoint light monitoring is demonstrated with a sensitivity of -30 dBm and a dynamic range of 40 dB. CLIPP technology is simple, inherently CMOS compatible, and scalable to hundreds of probing points per chip. This concept provides a viable way to real-time conditioning and feedback control of densely-integrated photonic systems.

physics.optics↗

Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources

In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding Social Planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. The Lagrange multiplier takes the form of a nonnegative optional random measure on [0,T] which is flat off the set of times for which the constraint is binding, i.e. when all the fuel is spent. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank (2005). In the infinite-horizon case, with operating profit functions of Cobb-Douglas type, our method allows the explicit calculation of the optimal policy in terms of the `base capacity' process, i.e. the unique solution of the Bank and El Karoui representation problem (2004).

math.OC↗

Power Series Representations for European Option Prices under Stochastic Volatility Models

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset price process and the volatility process. We first obtain expressions for the power series' coefficients from the generalized Hull and White formula obtained by Elisa Alòs. Afterwards, we provide representations turning out from the approach for the sensitivity problem tackled by Malliavin calculus techniques, and these allow to handle not only vanilla options. Finally, we show the numerical performance of the associated Monte Carlo estimators for several stochastic volatility models.

q-fin.PR↗

Measuring the Temperature of a Mesoscopic Quantum Electron System by means of Single Electron Statistics

We measure the temperature of a mesoscopic system consisting of an ultra-dilute two dimensional electron gas at the $Si/SiO_2$ interface in a metal-oxide-semiconductor field effect transistor (MOSFET) quantum dot by means of the capture and emission of an electron in a point defect close to the interface. Contrarily to previous reports, we show that the capture and emission by point defects in Si n-MOSFETs can be temperature dependent down to 800 mK. As the finite quantum grand canonical ensemble model applies, the time domain charge fluctuation in the defect is used to determine the temperature of the few electron gas in the channel.

cond-mat.mes-hall↗

Time Dependent Inelastic Emission and Capture of Localized Electrons in Si n-MOSFETs Under Microwave Irradiation

Microwave irradiation causes voltage fluctuations in solid state nanodevices. Such an effect is relevant in atomic electronics and nanostructures for quantum information processing, where charge or spin states are controlled by microwave fields and electrically detected. Here the variation of the characteristic times of the multiphonon capture and emission of a single electron by an interface defect in submicron MOSFETs is calculated and measured as a function of the microwave power, whose frequency of the voltage modulation is assumed to be large if compared to the inverse of the characteristic times. The variation of the characteristic times under microwave irradiation is quantitatively predicted from the microwave frequency dependent stationary current generated by the voltage fluctuations itself. The expected values agree with the experimental measurements. The coupling between the microwave field and either one or two terminals of the device is discussed. Some consequences on nanoscale device technology are drawn.

cond-mat.mes-hall↗