Minimax hedging strategy

Static Hedging of Standard Options

BackgroundActive magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach ¼ of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to.MethodsFirst an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants.ResultsThe analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor.ConclusionThe worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q Vind < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q Vind > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for.

9106 Background: Most patients with advanced cancer want an idea of typical, best case, and worst case scenarios for overall survival (OS). Specific percentiles from OS curves of comparable patients are a reasonable starting point for estimating these scenarios. We summarized recent randomized trials to determine if simple multiples of the median OS from each curve provided reasonable estimates of these scenarios, and to determine the ratio of median OS to median PFS from corresponding curves. Methods: We searched the Cochrane register and major journals from 1999 to 2009 for randomized trials of first-line chemotherapy for MBC with ≥90 patients/arm. We recorded the median and following percentiles (represented scenario) from each OS curve: 90th (worst case), 75th (lower typical), 25th (upper typical) and 10th (best case). We estimated these percentiles for each OS curve by multiplying its median by the following simple multiples: 0.25 for the 90th, 0.5 for the 75th, 2 for the 25th, and 3 for the 10th. Each estimate was deemed accurate if within 0.75 to 1.33 times the actual value. Associations between trial characteristics and median OS were assessed with linear regression. Results: We analyzed 74 OS curves from 34 trials including 12,714 women followed for a median of 3 years. The average value (interquartile range, IQR) of the median OS was 22 months (18-24), of the median PFS was 7 months (6-9), and of the ratio of median OS to PFS was 3.0 (2.4-3.5). The average value (IQR) in months from all OS curves for each scenario was: worst case 6 (5-7), lower typical 12 (10-13), upper typical 36 (31-41) and best case 56 (47-60). Simple multiples of the median OS provided accurate estimates of the worst case in 75% of curves, lower typical in 97%, upper typical in 96% and best case in 96%. OS was longer in trials with a higher proportion of ER+ tumors (p=0.0018) and in trials of HER2+ women treated with trastuzumab (p=0.004). Conclusions: Worst, typical, and best case scenarios were remarkably consistent in a wide range of contemporary trials. Simple multiples of the median provided accurate estimates of these scenarios for most OS curves and are a good basis for discussing prognosis. No significant financial relationships to disclose.

We derive a risk‐neutral pricing model for discrete dynamic guaranteed funds with geometric Gaussian underlying security price process. We propose a dynamic hedging strategy by adding a gamma factor to the conventional delta. Simulation results demonstrate that, when hedging discretely, the risk‐neutral gamma‐adjusted‐delta strategy outperforms the dynamic delta hedging strategy by reducing the expected hedging error, lowering the hedging error variability, and improving the self‐financing possibility. The discrete dynamic delta‐only hedging not only causes potential overcharge to clients but also could be costly to the issuers. We show that a naive application of continuous‐time hedging formula to a discrete‐time hedging setting tends to worsen these possibilities.

When the underlying asset price depends on activities of traders, hedging errors include costs due to the illiquidity of the underlying asset and the size of this cost can be substantial. Cetin et al. (2004), Liquidity risk and arbitrage pricing theory, Finance and Stochastics, 8(3), 311-341, proposed a hedging strategy that approximates the classical Black–Scholes hedging strategy and produces zero liquidity costs. Here, we compute the rate of convergence of the final value of this hedging portfolio to the option payoff in case of a European call option; i.e. we see how fast its hedging error converges to zero. The hedging strategy studied here is meaningful due to its simple liquidity cost structure and its smoothness relative to the classical Black–Scholes delta.

Management of saltwater intrusion in coastal aquifers should be based on robust management strategies and monitoring of their impacts. A robust optimal management strategy is less sensitive to deviations from prescribed strategies at the field level. Development of robust management framework is an important issue that needs attention especially when it results in near optimal strategies even when deviations from prescribed strategies occur in the field implementation stage. Implementation of a strategy requires field scale monitoring to determine the impact in terms of compliance with management goals due to possible deviation from an optimal prescribed strategy. Design of such an optimal monitoring network for compliance also requires robust optimal design due to the uncertainties involved. Deviations from prescribed strategies in the field are often more sensitive to uncertainties in the implementation phase. A multiple objective management model for robust optimal management of saltwater intrusion in coastal aquifers is proposed. Both risk neutral and risk-based management model formulations are presented. A robust monitoring network design methodology is also proposed for compliance monitoring of proposed robust management strategies. Performances of the developed methodology are tested for an illustrative coastal aquifer study area, as presented by Dhar and Datta. Performance evaluations show potential applicability of the developed methodologies and some of the relative advantages.

Delta hedging in discrete time under stochastic interest rate

Incorporating adjuvant cyclin-dependent kinase (CDK) 4/6 inhibitors abemaciclib and ribociclib along with endocrine therapy has been shown to improve invasive disease-free survival (iDFS) for hormone receptor-positive (HR+) human epidermal receptor 2-negative (HER2-) early breast cancer (EBC). This study assesses the cost-effectiveness of this strategy, along with adjuvant aromatase inhibitors from an Indian perspective. A Markov chain model evaluated the cost-effectiveness of abemaciclib and ribociclib with letrozole compared with letrozole alone for HR+/HER2- EBC from a payer perspective in India. Key measures included lifetime quality-adjusted life-years (QALY), life-years (LY), and total costs. This study explores two scenarios for effectiveness: a best-case (BC) scenario, where the benefit of CDK4/6 inhibitors in improving iDFS lasts a lifetime, and a worst-case (WC) scenario, where benefits disappear after 5 years. Probabilistic sensitivity analyses (PSA) were used to account for simulation uncertainty. In the BC scenario, abemaciclib added 2.17 QALY and 4.96 LY, incurring ₹2,317,957.7 ($27,756.65 in US dollars [USD]) in additional costs. However, the incremental cost-effectiveness ratio (ICER) for abemaciclib exceeded India's willingness-to-pay threshold in the BC and WC scenarios. In the BC scenario, ribociclib added 0.98 QALY and 2.58 LY with added costs of ₹1,711,504.32 ($20,494.6 USD). The ICER for ribociclib also surpassed India's threshold in both scenarios. PSA showed that neither drug was cost-effective at the current market prices in either BC/WC scenario. The cost of abemaciclib and ribociclib needs to be reduced by at least 78.61% and 87.19%, respectively, to be cost-effective in the BC scenario. The combination of adjuvant abemaciclib or ribociclib with letrozole is not cost-effective for HR+/HER2- EBC in India in either the BC or WC scenario.

In this paper, using high-frequency intra-daily data from the UK market, we employ genetic programming (GP) to uncover a hedging strategy for FTSE 100 call options, hedged using FTSE 100 futures contracts. The output from the evolved strategies is a rebalancing signal which is conditioned upon a range of dynamic non-linear factors related to market conditions including liquidity and volatility. When this signal exceeds threshold values during the trading day, the hedge position is rebalanced. The performance of the GP-evolved strategy is evaluated against a number of commonly used, time-based, deterministic hedging strategies where the hedge position is rebalanced at fixed time intervals ranging from 5 min to 1 day. Assuming the delta hedger pays the bid-ask spread on the futures contract whenever the portfolio is rebalanced, this study finds that the GP-evolved hedging strategy out-performs standard, deterministic, time-based approaches. Empirical analysis shows that the superior performance of the GP strategy is driven by its ability to account for non-linear intra-day persistence in high frequency measures of liquidity and volatility. This study is the first to apply a GP methodology for the task of delta hedging with high frequency data, a significant risk management issue for investors and market makers in financial options.

A dam break is a low-probability, high risk catastrophe event that is extremely destructive and has a substantial negative socio-economic impact on downstream and nearby areas. Simulating dam breach and analyzing flood propagation downstream from those events is vital for identifying and minimizing the risks associated downstream of dam location. This study is intended to anlayse the effect of overtopping failure of dam for two scenario (a) base-case scenario (scenario with average value of dam breach parameters from their range) and (b) worst case scenario (the breach with largest geometry, shortest formation time and highest peak outflow magnitude). Further, a hydrodyanmic modelling is perfomed to investigate the sensitivity analysis (local and global) of five dam breach parameters (dam breach elevation, dam breach width, breach formation time, weir coefficient, trigger failure elevation) on breach outflow in a proposed hydropower project located in Nepal. Aeronautical Reconnaissance Coverage Geographic Information System (ArcGIS), Hydraulic Engineering Center River Analysis System (HEC-RAS) and OriginPro 2022b are utilized to analyse the effect of dam breach and parameter sensitivity. Generation of outflow hydrograph shows that worst case scenario has devasting effect downstream with innudation of 1047 of househols and 50.83 kilometers of roads. The breach velocty was recorded as 15.16 m/s and 20.85 m/s for base and worst case respectively. The minimum depth and maximum depth of flooding downstream from dam location was found to be 24.51 m and 73.6 m for base case and 47.43 m and 106.75 m for worst case. Due to backwater effect at Bheri river, peak flow at 14 km downstream from dam reduces significantly to 124852.57 m3/s and 244204.41 m3/s for base and worst case respectively. From local sensitivty analysis it has been found that, dam breach elevation is more sensitive and triggering failure elevation is less sensitive for peak outflow hydrograph. Whereas, dam breach width seems more sensitive and TFE seems least sensitive for peak outflow using Monte Carlo Simulation for gloal sensitivity.

International audience

As the advance of memory technologies, multiple types of memory such as different kinds of non-volatile memory (NVM), SRAM, DRAM, etc. provide a flexible configuration considering performance, energy and cost. For improving the performance of systems with multiple types of memory, data allocation is one of the most important tasks. The previous studies on data allocation problem assume the worst (fixed) case of data-access frequencies. However, the data allocation produced by employing worst case usually leads to an inferior performance for most of time. In this paper, we model this problem by probabilities and design efficient algorithms that can give optimal-cost data allocation with a guaranteed probability. The proposed DAGP algorithm produces a set of feasible data allocation solutions which generates the minimum access time or cost guaranteed by a given probability. The experiments show that our technique can significantly reduce the access time or cost compared with the technique considering worst case scenario. For example, comparing with the optimal result generated by employing the worst cases, our technique can reduce memory access time by 10.35% on average when guaranteed probability is set to be 0.8. Moreover, for 80 percents of cases, memory access time is reduced by 23.98% on average.

ABSTRACT: Conventional knowledge of market volatility represents that two proximate financial markets operated in the same country would display a similar pattern in their time-varying volatility. In this paper, we propose that the heterogeneity in financial policy orientation of stock markets creates significant inter-market differences in terms of the volatility of stock returns, even if they are culturally and geographically linked to each other. For the empirical investigation of our proposition, the volatility data from two major stock exchanges in the Middle East, the Abu Dhabi Securities Exchange (ADX) and the Dubai Financial Market (DFM) are used. Both the ADX and DFM stock exchanges operate in the same country, the United Arab Emirates (UAE). The ADX is based in Abu Dhabi, the administrative capital, while the DFM is based in Dubai, the commercial and business hub of the UAE. They were both established in the year 2000, and their operational headquarters are located about 150 km from each other. This paper uses a multivariate GARCH model, in particular a diagonal VECH GARCH (1, 1) model to estimate volatility measures for stock returns between ADX-listed and DFM-listed stocks. The paper finds that the stock returns are significantly less volatile in the ADX compared to those in the DFM suggesting that the volatility transmission is incomplete between these two neighboring financial markets. This difference in volatility can potentially be attributed to the relatively conservative financial policies adopted by the oil-rich emirate of Abu Dhabi compared to the more market-oriented economic policies of Dubai, the country’s financial and commercial hub. Our findings have considerable implications for portfolio managers in ascertaining risk premiums when allocating investments across the two stock exchanges. For instance, this disparity in volatility should be taken into account by investors and policymakers when designing risk management strategies because it suggests that investors in the DFM may be exposed to higher levels of risk and uncertainty compared to their counterparts in the ADX. Investors operating in the DFM may require more robust risk management strategies, such as asset diversification and hedging, compared to their ASX counterparts.

This paper investigates trends of historical and projected future South African coal-fired power station criteria (total primary Particulate Matter (PM), Sulphur Dioxide (SO2) and Nitrogen Oxides (NOx)) and Carbon Dioxide (CO2) emissions. It was found that an energy restricted environment has an increasing effect on emissions, as emissions per energy unit increased from the onset of the South African energy crisis. PM emissions particularly, increased during the energy crisis period, due to increased pressure on PM abatement and lowered maintenance opportunity. Projections of future coal-fired power station criteria and CO2 emissions are made for four different future scenarios for the period 2015 to 2030. Three of the four scenarios are based on the lower projected energy demand baseline case as published in the updated Integrated Development Plan (IRP). The difference between these three scenarios is different retrofit rates of power stations with emissions abatement technologies. The fourth scenario is a worst case scenario and assumes high energy demand (and therefore no decommissioning of power stations), high emission rates (similar to worst past emission rates during the period 1999-2012) and no further abatement of emissions above and beyond current mitigation efforts. This scenario gives an indication of what South African coal-fired power station emissions could look like if the energy crisis persists. There is a marked difference between projected best and worst case PM emissions during the entire projected period, but especially during 2030 when worst case PM emissions compared to a 2015 baseline value are expected to rise by 40% and best case PM emissions are projected to decline by 40%. Worst case NOx emissions are expected to increase by 40% in 2030 from a 2015 baseline value whereas best case emissions are expected to decline 10% from the same level in 2030. Worst case SO2 emissions are predicted to increase by around 38% in 2030 and best case emissions are expected to decrease by around 20% in 2030 from a 2015 baseline value. Relative emissions used in the projection of future CO2 emissions in this paper differ from that used in the energy demand and energy mix modelling done for the updated IRP baseline case. The reason for this is that the modelling for the updated IRP assumed relative CO2 emission factors for supercritical boilers, whereas only Kusile and Medupi fall in this category and relative emissions from all other stations are, in fact, between 5% and 16% higher. For this reason, it seems unlikely that the South African climate commitment target for 2030 will be made.

Analysis of Worst Case Stochastic Link Capacity Degradation to Aid Assessment of Transportation Network Reliability