Radio access network based positioning and ranging technologies become more and more important for autonomous driving. Positioning on the 5G Sidelink (SL) is discussed in Release 18 (2022-2024) of the Third Generation Partnership Project. For accurate timing-based ranging, a high temporal and spatial resolution is fundamental. The bandwidth for 5G SL positioning is limited due to sharing the existing SL resources with communication. Therefore, we send the positioning reference signal on two separate Component Carriers, i.e. we use a fragmented spectrum. We introduce a two step algorithm for estimating the time of arrival using the inflection point method. We proved a fragmented spectrum can achieve the same accuracy as a continuous spectrum.

We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to evolve according to a geometric Lévy process. We prove that the asymptotic behavior of the ruin probability depends to a large extent only on the properties of the price process.

Positioning benefits from channel models that capture geometric effects and, in particular, from the signal properties of the first arriving path and the spatial consistency of the propagation condition of multiple links. The models that capture the physical effects observed in a realistic deployment scenario are essential for assessing the potential benefits of enhancements in positioning methods. Channel models based on ray-tracing simulations and statistical channel models, which are current state-of-the-art methods employed to evaluate performance of positioning in 3GPP systems, do not fully capture important aspects applicable to positioning. Hence, we propose an extension of existing statistical channel models with semi-deterministic clusters (SDCs). SDCs allow channels to be simulated using three types of clusters: fixed-, specular-, and random-clusters. Our results show that the proposed model aligns with measurements obtained in a real deployment scenario. Thus, our channel models can be used to develop advanced positioning solutions based on machine learning, which enable positioning with centimeter level accuracy in NLOS and multipath scenarios.

Physical effects such as reflection, refraction, and diffraction cause a radio signal to arrive from a transmitter to a receiver in multiple replicas that have different amplitude and rotation. Bandwidth-limited signals, such as positioning reference signals, have a limited time resolution. In reality, the signal is often reflected in the close vicinity of a transmitter and receiver, which causes the displacement of the observed peak from the true peak expected according to the line of sight (LOS) geometry between the transmitter and receiver. In this paper, we show that the existing channel model specified for performance evaluation within 3GPP fails to model the above phenomena. As a result, the simulation results deviate significantly from the measured values. Based on our measurement and simulation results, we propose a model for incorporating the signal reflection by obstacles in the vicinity of transmitter or receiver, so that the outcome of the model corresponds to the measurement made in such scenario.

Standardization of New Radio (NR) in the third generation partnership project (3GPP) introduced staggered reference signal transmission for positioning. Staggering facilitates unambiguously reaching base stations at larger distances in power-limited scenarios in the uplink. When linear phase is applied to a base sequence in the frequency domain, this translates to the time shifted version of the corresponding sequence in the time domain. This property enables an efficient assignment of resources to multiple user equipments (UEs) or antenna ports. In this paper, we address the issue of interference arising from multiplexing UEs or antenna ports using cyclic shift in scenarios where reference signals are transmitted using a staggered pattern. An evaluation of the effects shows that non-linear phase and limited range of the search window based on the Rel. 16 sounding reference signal (SRS) design causes false detection and erroneous Time of Arrival (ToA) estimates, which impairs the positioning accuracy. A solution is proposed by applying phase correction and range extension to existing base sequences, thereby ensuring backward compatibility of existing network elements. We show that the proposed approach provides more reliable ToA estimates. System level simulations demonstrate that the proposed solution mitigates these effects compared to the state-of-the-art mechanism.

Driven by an ever-increasing demand for higher data rates, 5G introduced communication over the millimeter-wave (mmWave) bands to fulfill this requirement. High data transmissions in this spectrum are enabled by beamforming massive MIMO antennas and the available allocated bandwidth. Of interest is the utilization of mmWave for high-accuracy positioning applications, motivated by the allocated bandwidth and beamforming characteristics of such systems. This paper provides numerical simulations on the 5G positioning reference signal reception and shows, for a real-world indoor environment, positioning performance results. The accuracy of ToA-based positioning in dependence of the beam shape and direction is determined to be at least within 6 cm for LOS scenarios. We also investigate the impact of LOS path obstructions on the performance. Achieving centimeter level accuracy is subject to improvements through continuing research and refinements.

Many radio-based positioning systems use time-ofarrival (ToA). We obtain it from the first and direct path of arrival (FDPoA) in a corresponding set of multipath components (MPC) of the underlying channel state information (CSI). While detection of the FDPoA under Line-of-Sight (LoS) is simple, it is prone to errors in environments with specular and diffuse reflections, as well as nonlinear diffraction, absorption, and transmission of a signal. Such Obstructedor Non-Line-ofSight (OLoS, NLoS) situations lead to incorrect FDPoA and consequently to incorrect ToA estimates and inaccurate positions. State-of-the-art estimators are computationally expensive and usually fail with O/NLoS at low signal-to-noise ratios (SNRs). We propose a deep learning (DL) approach to identify optimal FDPoAs as ToA directly from the raw CSI. Our 1D Convolutional Neural Network (CNN) learns the spatial distribution of MPCs of the CSI to predict correct estimates of the ToA. To train our DL model, we use QuaDRiGa to generate datasets with CIRs and ground truth ToAs for realistic 5G channel models. We found that Delay Spread (DS), k-Factor (kF), and SNR are appropriate metrics to cover most LoS-NLoS constellations in realistic datasets. We compare our DL model with state-of-theart estimators such as threshold (PEAK), inflection point (IFP), and MUSIC and show that we consistently outperform them by about 17% for SNRs below -10 dB.

This paper proposes a framework for the valuation and the management of complex life insurance contracts, whose design can be described by a portfolio of embedded options, which are activated according to one or more triggering events. These events are in general monitored discretely over the life of the policy, due to the contract terms. Similar designs can also be found in other contexts, such as counterparty credit risk for example. The framework is based on Fourier transform methods as they allow to derive convenient closed analytical formulas for a broad spectrum of underlying dynamics. Multidimensionality issues generated by the discrete monitoring of the triggering events are dealt with efficiently designed Monte Carlo integration strategies. We illustrate the tractability of the proposed approach by means of a detailed study of ratchet variable annuities, which can be considered a prototypical example of these complex structured products.

ABSTRACT In this paper, we develop an arbitrage-free multiple curve model through the specification of forward swap rates. Two sets of assets are chosen as fundamentals: OIS zero-coupon bonds and forward rate agreements. This is a very natural approach since, on the one hand, OIS bonds represent the class of risk-free discount bonds and, on the other hand, the mid and long maturity part of the interest rate term structure is bootstrapped from quotes of swap rates that can be represented by FRA rates and OIS bond prices in the multiple curve setting. We construct the rates via a backward induction along the tenor structure on the basis of the forward swap measures. Time-inhomogeneous Lévy processes are used as drivers of the dynamics. As an application, we derive an approximative Fourier-based valuation formula for swaptions. The model is implemented and calibrated by using generalized hyperbolic Lévy processes as drivers.

In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are simplified significantly. These properties make it an excellent base for a post-crisis multiple curve setup. Two variants for multiple curve constructions are discussed. Time-inhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Based on the valuation formula, we calibrate the two model variants to market data.

This paper proposes a market consistent valuation framework for variable annuities (VAs) with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the fair value of the VA and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.

Valuation based on quadratic hedging is easy to understand and mathematically tractable compared to other approaches. Its economic justification is less obvious.

In Sect. 11.3 we discussed pricing and hedging of OTC derivatives from the option writer’s point of view. The approach was based on arbitrage arguments.

The theory of Mathematical Finance in the following chapters rests on price processes of assets such as stocks, currencies, bonds, and commodities. They are often assumed to be given exogenously. Therefore we start by discussing what kinds of processes are suggested by statistical properties of real data.

The continuous-time analogue of a random walk is called a Lévy process. One may also view Lévy processes as the stochastic counterpart of linear functions. Both viewpoints illustrate that these processes play a fundamental role.